What does this notation in this SAT-Test question mean?

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I am teaching a student for SAT and I find the following problem. I have no idea what the notation $$
fboxk=left(-k,frack2right)$$ means. Could you elaborate it more detailed?



The question reads:




$fboxk = left(-k, frack2right)$ where $k$ is an integer. What is the equation of the line passing through $fboxk$?



A. $y = 2x + 2$



B. $y = 2x$



C. $y = -2x$



D. $y = frac12x - 2$



E. $y = - frac12x$





notation parametric




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  • 25




    I was seriously confused to find out this is not in any way related to the boolean satisfiability problem.
    – lisyarus
    Aug 3 at 16:49










  • Is this an official CollegeBoard SAT question or one made from a third party test prep company? I've tutored SAT for years, and while they enjoy "weird notation" questions, this one doesn't quite feel like CollegeBoard's style.
    – zahbaz
    Aug 4 at 6:50






  • 3




    "What is the equation of the line passing through [k]?" is not a logical question in this context. Because many lines can pass through the points represent by (−k,k/2). And in other to exclusively associate the line with the point, more data would be needed, for instance the gradient.
    – Igwe Kalu
    2 days ago











  • @zahbaz: McGraw-Hill's Conquering SAT 2nd edition on page 264.
    – Field Medalist
    2 days ago










  • @xport Okay, cool. McGraw-Hill usually has good practice problems. The actual SAT is often a bit more deliberate when introducing new notation.
    – zahbaz
    2 days ago














up vote
14
down vote

favorite












I am teaching a student for SAT and I find the following problem. I have no idea what the notation $$
fboxk=left(-k,frack2right)$$ means. Could you elaborate it more detailed?



The question reads:




$fboxk = left(-k, frack2right)$ where $k$ is an integer. What is the equation of the line passing through $fboxk$?



A. $y = 2x + 2$



B. $y = 2x$



C. $y = -2x$



D. $y = frac12x - 2$



E. $y = - frac12x$





notation parametric




share|cite|improve this question

















  • 25




    I was seriously confused to find out this is not in any way related to the boolean satisfiability problem.
    – lisyarus
    Aug 3 at 16:49










  • Is this an official CollegeBoard SAT question or one made from a third party test prep company? I've tutored SAT for years, and while they enjoy "weird notation" questions, this one doesn't quite feel like CollegeBoard's style.
    – zahbaz
    Aug 4 at 6:50






  • 3




    "What is the equation of the line passing through [k]?" is not a logical question in this context. Because many lines can pass through the points represent by (−k,k/2). And in other to exclusively associate the line with the point, more data would be needed, for instance the gradient.
    – Igwe Kalu
    2 days ago











  • @zahbaz: McGraw-Hill's Conquering SAT 2nd edition on page 264.
    – Field Medalist
    2 days ago










  • @xport Okay, cool. McGraw-Hill usually has good practice problems. The actual SAT is often a bit more deliberate when introducing new notation.
    – zahbaz
    2 days ago












up vote
14
down vote

favorite









up vote
14
down vote

favorite











I am teaching a student for SAT and I find the following problem. I have no idea what the notation $$
fboxk=left(-k,frack2right)$$ means. Could you elaborate it more detailed?



The question reads:




$fboxk = left(-k, frack2right)$ where $k$ is an integer. What is the equation of the line passing through $fboxk$?



A. $y = 2x + 2$



B. $y = 2x$



C. $y = -2x$



D. $y = frac12x - 2$



E. $y = - frac12x$





notation parametric




share|cite|improve this question













I am teaching a student for SAT and I find the following problem. I have no idea what the notation $$
fboxk=left(-k,frack2right)$$ means. Could you elaborate it more detailed?



The question reads:




$fboxk = left(-k, frack2right)$ where $k$ is an integer. What is the equation of the line passing through $fboxk$?



A. $y = 2x + 2$



B. $y = 2x$



C. $y = -2x$



D. $y = frac12x - 2$



E. $y = - frac12x$






notation parametric





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share|cite|improve this question




share|cite|improve this question








edited 2 days ago









Adrian

5,1791035




5,1791035









asked Aug 3 at 13:58









Field Medalist

2028




2028







  • 25




    I was seriously confused to find out this is not in any way related to the boolean satisfiability problem.
    – lisyarus
    Aug 3 at 16:49










  • Is this an official CollegeBoard SAT question or one made from a third party test prep company? I've tutored SAT for years, and while they enjoy "weird notation" questions, this one doesn't quite feel like CollegeBoard's style.
    – zahbaz
    Aug 4 at 6:50






  • 3




    "What is the equation of the line passing through [k]?" is not a logical question in this context. Because many lines can pass through the points represent by (−k,k/2). And in other to exclusively associate the line with the point, more data would be needed, for instance the gradient.
    – Igwe Kalu
    2 days ago











  • @zahbaz: McGraw-Hill's Conquering SAT 2nd edition on page 264.
    – Field Medalist
    2 days ago










  • @xport Okay, cool. McGraw-Hill usually has good practice problems. The actual SAT is often a bit more deliberate when introducing new notation.
    – zahbaz
    2 days ago












  • 25




    I was seriously confused to find out this is not in any way related to the boolean satisfiability problem.
    – lisyarus
    Aug 3 at 16:49










  • Is this an official CollegeBoard SAT question or one made from a third party test prep company? I've tutored SAT for years, and while they enjoy "weird notation" questions, this one doesn't quite feel like CollegeBoard's style.
    – zahbaz
    Aug 4 at 6:50






  • 3




    "What is the equation of the line passing through [k]?" is not a logical question in this context. Because many lines can pass through the points represent by (−k,k/2). And in other to exclusively associate the line with the point, more data would be needed, for instance the gradient.
    – Igwe Kalu
    2 days ago











  • @zahbaz: McGraw-Hill's Conquering SAT 2nd edition on page 264.
    – Field Medalist
    2 days ago










  • @xport Okay, cool. McGraw-Hill usually has good practice problems. The actual SAT is often a bit more deliberate when introducing new notation.
    – zahbaz
    2 days ago







25




25




I was seriously confused to find out this is not in any way related to the boolean satisfiability problem.
– lisyarus
Aug 3 at 16:49




I was seriously confused to find out this is not in any way related to the boolean satisfiability problem.
– lisyarus
Aug 3 at 16:49












Is this an official CollegeBoard SAT question or one made from a third party test prep company? I've tutored SAT for years, and while they enjoy "weird notation" questions, this one doesn't quite feel like CollegeBoard's style.
– zahbaz
Aug 4 at 6:50




Is this an official CollegeBoard SAT question or one made from a third party test prep company? I've tutored SAT for years, and while they enjoy "weird notation" questions, this one doesn't quite feel like CollegeBoard's style.
– zahbaz
Aug 4 at 6:50




3




3




"What is the equation of the line passing through [k]?" is not a logical question in this context. Because many lines can pass through the points represent by (−k,k/2). And in other to exclusively associate the line with the point, more data would be needed, for instance the gradient.
– Igwe Kalu
2 days ago





"What is the equation of the line passing through [k]?" is not a logical question in this context. Because many lines can pass through the points represent by (−k,k/2). And in other to exclusively associate the line with the point, more data would be needed, for instance the gradient.
– Igwe Kalu
2 days ago













@zahbaz: McGraw-Hill's Conquering SAT 2nd edition on page 264.
– Field Medalist
2 days ago




@zahbaz: McGraw-Hill's Conquering SAT 2nd edition on page 264.
– Field Medalist
2 days ago












@xport Okay, cool. McGraw-Hill usually has good practice problems. The actual SAT is often a bit more deliberate when introducing new notation.
– zahbaz
2 days ago




@xport Okay, cool. McGraw-Hill usually has good practice problems. The actual SAT is often a bit more deliberate when introducing new notation.
– zahbaz
2 days ago










3 Answers
3






active

oldest

votes

















up vote
20
down vote



accepted










It appears that $fboxk$ denotes a point (in this case, the point $(-k, k/2)$ for some integer $k$). It is not a notation I have ever seen before -- I would expect something like $P_k = (-k, k/2)$) -- but there is no accounting for taste.



(Although it wasn't in your question, the correct answer to the SAT question is then E: the line $y = -frac12x$ contains the point $ fboxk = (-k, k/2)$ for every integer $k$.)






share|cite|improve this answer

















  • 6




    That it is new notation is the point.
    – Acccumulation
    Aug 3 at 19:00










  • @Acccumulation, the new notation is a point. :)
    – Joel Reyes Noche
    2 days ago


















up vote
25
down vote













You're always allowed to invent notation, as long as you explain what it means. Tests like the SAT like to do this to test if you're really comfortable with the ideas in abstract sense, and not tied to any particular notation.



But I have some objections to the way this is worded. The first sentence




$fboxk = (-k, frack2)$, where $k$ is an integer




seems to imply that $k$ is a single unknown value, so $fboxk$ is a single point. But then there are an infinite number of lines through that point, so the question should be "which of these lines goes through that point?". The wording of the question seems to indicate that $fboxk$ is a function defined on the integers, but then the question should say something like "... passing through all points $fboxk$".






share|cite|improve this answer

















  • 4




    I have similar reservations about this question. "The wording of the question seems to indicate that $fbox k$ is a function defined on the integers". Well, no, it doesn't suggest that $fbox k$ is a function, it suggests that $fbox $ is a function. If we had $f(k) = (-k,frac k2)$, $f$ would be a function. $f(k)$ is not a function, it's a fixed value. I guess that "What is the equation of the set of points obtained by taking $fbox k$ over all $k$?" would work, or "Which of these lines do we know for certain goes through $fbox k$, without knowing what k is?"
    – Acccumulation
    Aug 3 at 19:16










  • True, if k==0, Answers B,C,E work. If k=-1D,E works.
    – chux
    Aug 4 at 5:29

















up vote
1
down vote













As MattPutnam explains in his answer, this question is asking the student to quickly adapt to a made-up notation.



The particular notation describes a "parametric equation":



$fboxk$ defines an input parameter k, and an output point named $fboxk$.



In this particular example:



  • The input is k, which can be any integer.

  • Thus, the student can choose from an infinite number of examples, and can even graph them.

  • The output (for any given value of k) is the point (-k, k/2).

You can think of the set of points (-k, k/2) : k ϵ Z as being a parametric equation of a set of (x, y) points along a line, where x and y have values determined by the parameter k.



To solve this question, set x = -k, and y = k/2. Either check each proposed answer by substitution (CBS), or solve for y in terms of x:



x = -k.
k = -x.
y = -x/2.
Answer E is correct.
CBS:
y ≟ -x/2
k/2 ≟ -(-k)/2
k/2 = k/2
Confirmed that Answer E is correct.


Alternatively, the student could choose a value of k, evaluate $fboxk$, perform a CBS for each answer, and repeat until only one answer passed the CBS. For example:




CBS:

Suppose k = 0.

$fboxk$ = (0, 0)

A is wrong: (0, 2) ≠ (0, 0).

D is wrong: (0, -2) ≠ (0, 0).

B, C, and E are still possible: (0, 0) = (0, 0).



Suppose k = 2.

$fboxk$ = (-2, 1)

B is wrong: 1 ≠ 2*(-2).

C is wrong: 1 ≠ -2*(-2).

E is OK: 1 = (-1/2)*(-2).



Therefore Answer E is correct.







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    3 Answers
    3






    active

    oldest

    votes








    3 Answers
    3






    active

    oldest

    votes









    active

    oldest

    votes






    active

    oldest

    votes








    up vote
    20
    down vote



    accepted










    It appears that $fboxk$ denotes a point (in this case, the point $(-k, k/2)$ for some integer $k$). It is not a notation I have ever seen before -- I would expect something like $P_k = (-k, k/2)$) -- but there is no accounting for taste.



    (Although it wasn't in your question, the correct answer to the SAT question is then E: the line $y = -frac12x$ contains the point $ fboxk = (-k, k/2)$ for every integer $k$.)






    share|cite|improve this answer

















    • 6




      That it is new notation is the point.
      – Acccumulation
      Aug 3 at 19:00










    • @Acccumulation, the new notation is a point. :)
      – Joel Reyes Noche
      2 days ago















    up vote
    20
    down vote



    accepted










    It appears that $fboxk$ denotes a point (in this case, the point $(-k, k/2)$ for some integer $k$). It is not a notation I have ever seen before -- I would expect something like $P_k = (-k, k/2)$) -- but there is no accounting for taste.



    (Although it wasn't in your question, the correct answer to the SAT question is then E: the line $y = -frac12x$ contains the point $ fboxk = (-k, k/2)$ for every integer $k$.)






    share|cite|improve this answer

















    • 6




      That it is new notation is the point.
      – Acccumulation
      Aug 3 at 19:00










    • @Acccumulation, the new notation is a point. :)
      – Joel Reyes Noche
      2 days ago













    up vote
    20
    down vote



    accepted







    up vote
    20
    down vote



    accepted






    It appears that $fboxk$ denotes a point (in this case, the point $(-k, k/2)$ for some integer $k$). It is not a notation I have ever seen before -- I would expect something like $P_k = (-k, k/2)$) -- but there is no accounting for taste.



    (Although it wasn't in your question, the correct answer to the SAT question is then E: the line $y = -frac12x$ contains the point $ fboxk = (-k, k/2)$ for every integer $k$.)






    share|cite|improve this answer













    It appears that $fboxk$ denotes a point (in this case, the point $(-k, k/2)$ for some integer $k$). It is not a notation I have ever seen before -- I would expect something like $P_k = (-k, k/2)$) -- but there is no accounting for taste.



    (Although it wasn't in your question, the correct answer to the SAT question is then E: the line $y = -frac12x$ contains the point $ fboxk = (-k, k/2)$ for every integer $k$.)







    share|cite|improve this answer













    share|cite|improve this answer



    share|cite|improve this answer











    answered Aug 3 at 14:13









    Strants

    5,05421636




    5,05421636







    • 6




      That it is new notation is the point.
      – Acccumulation
      Aug 3 at 19:00










    • @Acccumulation, the new notation is a point. :)
      – Joel Reyes Noche
      2 days ago













    • 6




      That it is new notation is the point.
      – Acccumulation
      Aug 3 at 19:00










    • @Acccumulation, the new notation is a point. :)
      – Joel Reyes Noche
      2 days ago








    6




    6




    That it is new notation is the point.
    – Acccumulation
    Aug 3 at 19:00




    That it is new notation is the point.
    – Acccumulation
    Aug 3 at 19:00












    @Acccumulation, the new notation is a point. :)
    – Joel Reyes Noche
    2 days ago





    @Acccumulation, the new notation is a point. :)
    – Joel Reyes Noche
    2 days ago











    up vote
    25
    down vote













    You're always allowed to invent notation, as long as you explain what it means. Tests like the SAT like to do this to test if you're really comfortable with the ideas in abstract sense, and not tied to any particular notation.



    But I have some objections to the way this is worded. The first sentence




    $fboxk = (-k, frack2)$, where $k$ is an integer




    seems to imply that $k$ is a single unknown value, so $fboxk$ is a single point. But then there are an infinite number of lines through that point, so the question should be "which of these lines goes through that point?". The wording of the question seems to indicate that $fboxk$ is a function defined on the integers, but then the question should say something like "... passing through all points $fboxk$".






    share|cite|improve this answer

















    • 4




      I have similar reservations about this question. "The wording of the question seems to indicate that $fbox k$ is a function defined on the integers". Well, no, it doesn't suggest that $fbox k$ is a function, it suggests that $fbox $ is a function. If we had $f(k) = (-k,frac k2)$, $f$ would be a function. $f(k)$ is not a function, it's a fixed value. I guess that "What is the equation of the set of points obtained by taking $fbox k$ over all $k$?" would work, or "Which of these lines do we know for certain goes through $fbox k$, without knowing what k is?"
      – Acccumulation
      Aug 3 at 19:16










    • True, if k==0, Answers B,C,E work. If k=-1D,E works.
      – chux
      Aug 4 at 5:29














    up vote
    25
    down vote













    You're always allowed to invent notation, as long as you explain what it means. Tests like the SAT like to do this to test if you're really comfortable with the ideas in abstract sense, and not tied to any particular notation.



    But I have some objections to the way this is worded. The first sentence




    $fboxk = (-k, frack2)$, where $k$ is an integer




    seems to imply that $k$ is a single unknown value, so $fboxk$ is a single point. But then there are an infinite number of lines through that point, so the question should be "which of these lines goes through that point?". The wording of the question seems to indicate that $fboxk$ is a function defined on the integers, but then the question should say something like "... passing through all points $fboxk$".






    share|cite|improve this answer

















    • 4




      I have similar reservations about this question. "The wording of the question seems to indicate that $fbox k$ is a function defined on the integers". Well, no, it doesn't suggest that $fbox k$ is a function, it suggests that $fbox $ is a function. If we had $f(k) = (-k,frac k2)$, $f$ would be a function. $f(k)$ is not a function, it's a fixed value. I guess that "What is the equation of the set of points obtained by taking $fbox k$ over all $k$?" would work, or "Which of these lines do we know for certain goes through $fbox k$, without knowing what k is?"
      – Acccumulation
      Aug 3 at 19:16










    • True, if k==0, Answers B,C,E work. If k=-1D,E works.
      – chux
      Aug 4 at 5:29












    up vote
    25
    down vote










    up vote
    25
    down vote









    You're always allowed to invent notation, as long as you explain what it means. Tests like the SAT like to do this to test if you're really comfortable with the ideas in abstract sense, and not tied to any particular notation.



    But I have some objections to the way this is worded. The first sentence




    $fboxk = (-k, frack2)$, where $k$ is an integer




    seems to imply that $k$ is a single unknown value, so $fboxk$ is a single point. But then there are an infinite number of lines through that point, so the question should be "which of these lines goes through that point?". The wording of the question seems to indicate that $fboxk$ is a function defined on the integers, but then the question should say something like "... passing through all points $fboxk$".






    share|cite|improve this answer













    You're always allowed to invent notation, as long as you explain what it means. Tests like the SAT like to do this to test if you're really comfortable with the ideas in abstract sense, and not tied to any particular notation.



    But I have some objections to the way this is worded. The first sentence




    $fboxk = (-k, frack2)$, where $k$ is an integer




    seems to imply that $k$ is a single unknown value, so $fboxk$ is a single point. But then there are an infinite number of lines through that point, so the question should be "which of these lines goes through that point?". The wording of the question seems to indicate that $fboxk$ is a function defined on the integers, but then the question should say something like "... passing through all points $fboxk$".







    share|cite|improve this answer













    share|cite|improve this answer



    share|cite|improve this answer











    answered Aug 3 at 15:47









    MattPutnam

    44933




    44933







    • 4




      I have similar reservations about this question. "The wording of the question seems to indicate that $fbox k$ is a function defined on the integers". Well, no, it doesn't suggest that $fbox k$ is a function, it suggests that $fbox $ is a function. If we had $f(k) = (-k,frac k2)$, $f$ would be a function. $f(k)$ is not a function, it's a fixed value. I guess that "What is the equation of the set of points obtained by taking $fbox k$ over all $k$?" would work, or "Which of these lines do we know for certain goes through $fbox k$, without knowing what k is?"
      – Acccumulation
      Aug 3 at 19:16










    • True, if k==0, Answers B,C,E work. If k=-1D,E works.
      – chux
      Aug 4 at 5:29












    • 4




      I have similar reservations about this question. "The wording of the question seems to indicate that $fbox k$ is a function defined on the integers". Well, no, it doesn't suggest that $fbox k$ is a function, it suggests that $fbox $ is a function. If we had $f(k) = (-k,frac k2)$, $f$ would be a function. $f(k)$ is not a function, it's a fixed value. I guess that "What is the equation of the set of points obtained by taking $fbox k$ over all $k$?" would work, or "Which of these lines do we know for certain goes through $fbox k$, without knowing what k is?"
      – Acccumulation
      Aug 3 at 19:16










    • True, if k==0, Answers B,C,E work. If k=-1D,E works.
      – chux
      Aug 4 at 5:29







    4




    4




    I have similar reservations about this question. "The wording of the question seems to indicate that $fbox k$ is a function defined on the integers". Well, no, it doesn't suggest that $fbox k$ is a function, it suggests that $fbox $ is a function. If we had $f(k) = (-k,frac k2)$, $f$ would be a function. $f(k)$ is not a function, it's a fixed value. I guess that "What is the equation of the set of points obtained by taking $fbox k$ over all $k$?" would work, or "Which of these lines do we know for certain goes through $fbox k$, without knowing what k is?"
    – Acccumulation
    Aug 3 at 19:16




    I have similar reservations about this question. "The wording of the question seems to indicate that $fbox k$ is a function defined on the integers". Well, no, it doesn't suggest that $fbox k$ is a function, it suggests that $fbox $ is a function. If we had $f(k) = (-k,frac k2)$, $f$ would be a function. $f(k)$ is not a function, it's a fixed value. I guess that "What is the equation of the set of points obtained by taking $fbox k$ over all $k$?" would work, or "Which of these lines do we know for certain goes through $fbox k$, without knowing what k is?"
    – Acccumulation
    Aug 3 at 19:16












    True, if k==0, Answers B,C,E work. If k=-1D,E works.
    – chux
    Aug 4 at 5:29




    True, if k==0, Answers B,C,E work. If k=-1D,E works.
    – chux
    Aug 4 at 5:29










    up vote
    1
    down vote













    As MattPutnam explains in his answer, this question is asking the student to quickly adapt to a made-up notation.



    The particular notation describes a "parametric equation":



    $fboxk$ defines an input parameter k, and an output point named $fboxk$.



    In this particular example:



    • The input is k, which can be any integer.

    • Thus, the student can choose from an infinite number of examples, and can even graph them.

    • The output (for any given value of k) is the point (-k, k/2).

    You can think of the set of points (-k, k/2) : k ϵ Z as being a parametric equation of a set of (x, y) points along a line, where x and y have values determined by the parameter k.



    To solve this question, set x = -k, and y = k/2. Either check each proposed answer by substitution (CBS), or solve for y in terms of x:



    x = -k.
    k = -x.
    y = -x/2.
    Answer E is correct.
    CBS:
    y ≟ -x/2
    k/2 ≟ -(-k)/2
    k/2 = k/2
    Confirmed that Answer E is correct.


    Alternatively, the student could choose a value of k, evaluate $fboxk$, perform a CBS for each answer, and repeat until only one answer passed the CBS. For example:




    CBS:

    Suppose k = 0.

    $fboxk$ = (0, 0)

    A is wrong: (0, 2) ≠ (0, 0).

    D is wrong: (0, -2) ≠ (0, 0).

    B, C, and E are still possible: (0, 0) = (0, 0).



    Suppose k = 2.

    $fboxk$ = (-2, 1)

    B is wrong: 1 ≠ 2*(-2).

    C is wrong: 1 ≠ -2*(-2).

    E is OK: 1 = (-1/2)*(-2).



    Therefore Answer E is correct.







    share|cite|improve this answer



























      up vote
      1
      down vote













      As MattPutnam explains in his answer, this question is asking the student to quickly adapt to a made-up notation.



      The particular notation describes a "parametric equation":



      $fboxk$ defines an input parameter k, and an output point named $fboxk$.



      In this particular example:



      • The input is k, which can be any integer.

      • Thus, the student can choose from an infinite number of examples, and can even graph them.

      • The output (for any given value of k) is the point (-k, k/2).

      You can think of the set of points (-k, k/2) : k ϵ Z as being a parametric equation of a set of (x, y) points along a line, where x and y have values determined by the parameter k.



      To solve this question, set x = -k, and y = k/2. Either check each proposed answer by substitution (CBS), or solve for y in terms of x:



      x = -k.
      k = -x.
      y = -x/2.
      Answer E is correct.
      CBS:
      y ≟ -x/2
      k/2 ≟ -(-k)/2
      k/2 = k/2
      Confirmed that Answer E is correct.


      Alternatively, the student could choose a value of k, evaluate $fboxk$, perform a CBS for each answer, and repeat until only one answer passed the CBS. For example:




      CBS:

      Suppose k = 0.

      $fboxk$ = (0, 0)

      A is wrong: (0, 2) ≠ (0, 0).

      D is wrong: (0, -2) ≠ (0, 0).

      B, C, and E are still possible: (0, 0) = (0, 0).



      Suppose k = 2.

      $fboxk$ = (-2, 1)

      B is wrong: 1 ≠ 2*(-2).

      C is wrong: 1 ≠ -2*(-2).

      E is OK: 1 = (-1/2)*(-2).



      Therefore Answer E is correct.







      share|cite|improve this answer

























        up vote
        1
        down vote










        up vote
        1
        down vote









        As MattPutnam explains in his answer, this question is asking the student to quickly adapt to a made-up notation.



        The particular notation describes a "parametric equation":



        $fboxk$ defines an input parameter k, and an output point named $fboxk$.



        In this particular example:



        • The input is k, which can be any integer.

        • Thus, the student can choose from an infinite number of examples, and can even graph them.

        • The output (for any given value of k) is the point (-k, k/2).

        You can think of the set of points (-k, k/2) : k ϵ Z as being a parametric equation of a set of (x, y) points along a line, where x and y have values determined by the parameter k.



        To solve this question, set x = -k, and y = k/2. Either check each proposed answer by substitution (CBS), or solve for y in terms of x:



        x = -k.
        k = -x.
        y = -x/2.
        Answer E is correct.
        CBS:
        y ≟ -x/2
        k/2 ≟ -(-k)/2
        k/2 = k/2
        Confirmed that Answer E is correct.


        Alternatively, the student could choose a value of k, evaluate $fboxk$, perform a CBS for each answer, and repeat until only one answer passed the CBS. For example:




        CBS:

        Suppose k = 0.

        $fboxk$ = (0, 0)

        A is wrong: (0, 2) ≠ (0, 0).

        D is wrong: (0, -2) ≠ (0, 0).

        B, C, and E are still possible: (0, 0) = (0, 0).



        Suppose k = 2.

        $fboxk$ = (-2, 1)

        B is wrong: 1 ≠ 2*(-2).

        C is wrong: 1 ≠ -2*(-2).

        E is OK: 1 = (-1/2)*(-2).



        Therefore Answer E is correct.







        share|cite|improve this answer















        As MattPutnam explains in his answer, this question is asking the student to quickly adapt to a made-up notation.



        The particular notation describes a "parametric equation":



        $fboxk$ defines an input parameter k, and an output point named $fboxk$.



        In this particular example:



        • The input is k, which can be any integer.

        • Thus, the student can choose from an infinite number of examples, and can even graph them.

        • The output (for any given value of k) is the point (-k, k/2).

        You can think of the set of points (-k, k/2) : k ϵ Z as being a parametric equation of a set of (x, y) points along a line, where x and y have values determined by the parameter k.



        To solve this question, set x = -k, and y = k/2. Either check each proposed answer by substitution (CBS), or solve for y in terms of x:



        x = -k.
        k = -x.
        y = -x/2.
        Answer E is correct.
        CBS:
        y ≟ -x/2
        k/2 ≟ -(-k)/2
        k/2 = k/2
        Confirmed that Answer E is correct.


        Alternatively, the student could choose a value of k, evaluate $fboxk$, perform a CBS for each answer, and repeat until only one answer passed the CBS. For example:




        CBS:

        Suppose k = 0.

        $fboxk$ = (0, 0)

        A is wrong: (0, 2) ≠ (0, 0).

        D is wrong: (0, -2) ≠ (0, 0).

        B, C, and E are still possible: (0, 0) = (0, 0).



        Suppose k = 2.

        $fboxk$ = (-2, 1)

        B is wrong: 1 ≠ 2*(-2).

        C is wrong: 1 ≠ -2*(-2).

        E is OK: 1 = (-1/2)*(-2).



        Therefore Answer E is correct.








        share|cite|improve this answer















        share|cite|improve this answer



        share|cite|improve this answer








        edited 2 days ago


























        answered Aug 4 at 0:09









        Jasper

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