If a curve doesn't pass vertical line test, it's a not a function then is $x= |sin y|$ a function?

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My teacher told me if a vertical line intersects a curve more than once then the curve is NOT the graph of a function.



But what if I express $ x$ in terms of $y$? As in $x= f(y) $



Eg : $ x = left| sin y right|$
Graph



Clearly a vertical line $x = dfrac12$ intersects this curve more than once!



So is $x= | sin y | $ not a function?




functions




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  • $x$ is a function of $y$, but $y$ is not a function of $x$
    – rbird
    2 days ago










  • Check the well-definedness from the side of $y$
    – Anik Bhowmick
    2 days ago














up vote
0
down vote

favorite












My teacher told me if a vertical line intersects a curve more than once then the curve is NOT the graph of a function.



But what if I express $ x$ in terms of $y$? As in $x= f(y) $



Eg : $ x = left| sin y right|$
Graph



Clearly a vertical line $x = dfrac12$ intersects this curve more than once!



So is $x= | sin y | $ not a function?




functions




share|cite|improve this question



















  • $x$ is a function of $y$, but $y$ is not a function of $x$
    – rbird
    2 days ago










  • Check the well-definedness from the side of $y$
    – Anik Bhowmick
    2 days ago












up vote
0
down vote

favorite









up vote
0
down vote

favorite











My teacher told me if a vertical line intersects a curve more than once then the curve is NOT the graph of a function.



But what if I express $ x$ in terms of $y$? As in $x= f(y) $



Eg : $ x = left| sin y right|$
Graph



Clearly a vertical line $x = dfrac12$ intersects this curve more than once!



So is $x= | sin y | $ not a function?




functions




share|cite|improve this question











My teacher told me if a vertical line intersects a curve more than once then the curve is NOT the graph of a function.



But what if I express $ x$ in terms of $y$? As in $x= f(y) $



Eg : $ x = left| sin y right|$
Graph



Clearly a vertical line $x = dfrac12$ intersects this curve more than once!



So is $x= | sin y | $ not a function?





functions





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked 2 days ago









William

700214




700214











  • $x$ is a function of $y$, but $y$ is not a function of $x$
    – rbird
    2 days ago










  • Check the well-definedness from the side of $y$
    – Anik Bhowmick
    2 days ago
















  • $x$ is a function of $y$, but $y$ is not a function of $x$
    – rbird
    2 days ago










  • Check the well-definedness from the side of $y$
    – Anik Bhowmick
    2 days ago















$x$ is a function of $y$, but $y$ is not a function of $x$
– rbird
2 days ago




$x$ is a function of $y$, but $y$ is not a function of $x$
– rbird
2 days ago












Check the well-definedness from the side of $y$
– Anik Bhowmick
2 days ago




Check the well-definedness from the side of $y$
– Anik Bhowmick
2 days ago










1 Answer
1






active

oldest

votes

















up vote
0
down vote













$x$ is a function of $y$ but $y$ is not a function of $x$.



$y$ is not a function of $x$ has been explained by you.



For each value of $y$, we have a unique corresponding value, hence $x$ is a function of $y$ where the domain is $mathbbR$.






share|cite|improve this answer





















  • It is a function right? And it still fails vertical line test? How? Why?
    – William
    2 days ago










  • Depending on your reference of "it". $y$ is not a function of $x$. function is something that when you give it a a valid input, it return an output. now if you give $x=0.5$, there are so many values of $y$.
    – Siong Thye Goh
    2 days ago










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
0
down vote













$x$ is a function of $y$ but $y$ is not a function of $x$.



$y$ is not a function of $x$ has been explained by you.



For each value of $y$, we have a unique corresponding value, hence $x$ is a function of $y$ where the domain is $mathbbR$.






share|cite|improve this answer





















  • It is a function right? And it still fails vertical line test? How? Why?
    – William
    2 days ago










  • Depending on your reference of "it". $y$ is not a function of $x$. function is something that when you give it a a valid input, it return an output. now if you give $x=0.5$, there are so many values of $y$.
    – Siong Thye Goh
    2 days ago














up vote
0
down vote













$x$ is a function of $y$ but $y$ is not a function of $x$.



$y$ is not a function of $x$ has been explained by you.



For each value of $y$, we have a unique corresponding value, hence $x$ is a function of $y$ where the domain is $mathbbR$.






share|cite|improve this answer





















  • It is a function right? And it still fails vertical line test? How? Why?
    – William
    2 days ago










  • Depending on your reference of "it". $y$ is not a function of $x$. function is something that when you give it a a valid input, it return an output. now if you give $x=0.5$, there are so many values of $y$.
    – Siong Thye Goh
    2 days ago












up vote
0
down vote










up vote
0
down vote









$x$ is a function of $y$ but $y$ is not a function of $x$.



$y$ is not a function of $x$ has been explained by you.



For each value of $y$, we have a unique corresponding value, hence $x$ is a function of $y$ where the domain is $mathbbR$.






share|cite|improve this answer













$x$ is a function of $y$ but $y$ is not a function of $x$.



$y$ is not a function of $x$ has been explained by you.



For each value of $y$, we have a unique corresponding value, hence $x$ is a function of $y$ where the domain is $mathbbR$.







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered 2 days ago









Siong Thye Goh

76.5k134794




76.5k134794











  • It is a function right? And it still fails vertical line test? How? Why?
    – William
    2 days ago










  • Depending on your reference of "it". $y$ is not a function of $x$. function is something that when you give it a a valid input, it return an output. now if you give $x=0.5$, there are so many values of $y$.
    – Siong Thye Goh
    2 days ago
















  • It is a function right? And it still fails vertical line test? How? Why?
    – William
    2 days ago










  • Depending on your reference of "it". $y$ is not a function of $x$. function is something that when you give it a a valid input, it return an output. now if you give $x=0.5$, there are so many values of $y$.
    – Siong Thye Goh
    2 days ago















It is a function right? And it still fails vertical line test? How? Why?
– William
2 days ago




It is a function right? And it still fails vertical line test? How? Why?
– William
2 days ago












Depending on your reference of "it". $y$ is not a function of $x$. function is something that when you give it a a valid input, it return an output. now if you give $x=0.5$, there are so many values of $y$.
– Siong Thye Goh
2 days ago




Depending on your reference of "it". $y$ is not a function of $x$. function is something that when you give it a a valid input, it return an output. now if you give $x=0.5$, there are so many values of $y$.
– Siong Thye Goh
2 days ago












 

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