Mixing
understanding Multiplicity
Clash Royale CLAN TAG#URR8PPP
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in my books of algebra it talks about polynomial functions and their zeros
Multiplicity and x-Intercepts
If r is a zero of even multiplicity, then the graph touches the x-axis and turns
around at r. If r is a zero of odd multiplicity, then the graph crosses the x-axis
at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend
to flatten out near zeros with multiplicity greater than one.
what does flatten out means ?
algebra-precalculus
asked Jul 19 at 3:31
Ahmed M. Elsonbaty
474
add a comment |Â
up vote
2
down vote
favorite
in my books of algebra it talks about polynomial functions and their zeros
Multiplicity and x-Intercepts
If r is a zero of even multiplicity, then the graph touches the x-axis and turns
around at r. If r is a zero of odd multiplicity, then the graph crosses the x-axis
at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend
to flatten out near zeros with multiplicity greater than one.
what does flatten out means ?
algebra-precalculus
asked Jul 19 at 3:31
Ahmed M. Elsonbaty
474
Could you give us a little more context? What book is it, and what is the subject? The "zero" of what?
– Suzet
Jul 19 at 3:36
1
It means they don't grow very fast. Graph $y=x^n$ for some different values of $n$ on Wolfram Alpha, to see what the book means.
– saulspatz
Jul 19 at 3:37
zero of a polynomial function from book "Blitzer college algebra" Multiplicity and x-Intercepts If r is a zero of even multiplicity, then the graph touches the xaxis and turns around at r. If r is a zero of odd multiplicity, then the graph crosses the xaxis at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend to flatten out near zeros with multiplicity greater than one.
– Ahmed M. Elsonbaty
Jul 19 at 3:38
@AhmedM.Elsonbaty Compare for example the "flatness" of $x, x^2, x^3, x^4$ around $,x=0,$.
– dxiv
Jul 19 at 4:10
add a comment |Â
up vote
2
down vote
favorite
up vote
2
down vote
favorite
in my books of algebra it talks about polynomial functions and their zeros
Multiplicity and x-Intercepts
If r is a zero of even multiplicity, then the graph touches the x-axis and turns
around at r. If r is a zero of odd multiplicity, then the graph crosses the x-axis
at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend
to flatten out near zeros with multiplicity greater than one.
what does flatten out means ?
algebra-precalculus
asked Jul 19 at 3:31
Ahmed M. Elsonbaty
474
in my books of algebra it talks about polynomial functions and their zeros
Multiplicity and x-Intercepts
If r is a zero of even multiplicity, then the graph touches the x-axis and turns
around at r. If r is a zero of odd multiplicity, then the graph crosses the x-axis
at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend
to flatten out near zeros with multiplicity greater than one.
what does flatten out means ?
algebra-precalculus
asked Jul 19 at 3:31
Ahmed M. Elsonbaty
474
edited Jul 19 at 3:42
asked Jul 19 at 3:31
Ahmed M. Elsonbaty
474
asked Jul 19 at 3:31
Ahmed M. Elsonbaty
474
asked Jul 19 at 3:31
Ahmed M. Elsonbaty
474
474
Could you give us a little more context? What book is it, and what is the subject? The "zero" of what?
– Suzet
Jul 19 at 3:36
1
It means they don't grow very fast. Graph $y=x^n$ for some different values of $n$ on Wolfram Alpha, to see what the book means.
– saulspatz
Jul 19 at 3:37
zero of a polynomial function from book "Blitzer college algebra" Multiplicity and x-Intercepts If r is a zero of even multiplicity, then the graph touches the xaxis and turns around at r. If r is a zero of odd multiplicity, then the graph crosses the xaxis at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend to flatten out near zeros with multiplicity greater than one.
– Ahmed M. Elsonbaty
Jul 19 at 3:38
@AhmedM.Elsonbaty Compare for example the "flatness" of $x, x^2, x^3, x^4$ around $,x=0,$.
– dxiv
Jul 19 at 4:10
add a comment |Â
Could you give us a little more context? What book is it, and what is the subject? The "zero" of what?
– Suzet
Jul 19 at 3:36
1
It means they don't grow very fast. Graph $y=x^n$ for some different values of $n$ on Wolfram Alpha, to see what the book means.
– saulspatz
Jul 19 at 3:37
zero of a polynomial function from book "Blitzer college algebra" Multiplicity and x-Intercepts If r is a zero of even multiplicity, then the graph touches the xaxis and turns around at r. If r is a zero of odd multiplicity, then the graph crosses the xaxis at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend to flatten out near zeros with multiplicity greater than one.
– Ahmed M. Elsonbaty
Jul 19 at 3:38
@AhmedM.Elsonbaty Compare for example the "flatness" of $x, x^2, x^3, x^4$ around $,x=0,$.
– dxiv
Jul 19 at 4:10
Could you give us a little more context? What book is it, and what is the subject? The "zero" of what?
– Suzet
Jul 19 at 3:36
Could you give us a little more context? What book is it, and what is the subject? The "zero" of what?
– Suzet
Jul 19 at 3:36
1
1
It means they don't grow very fast. Graph $y=x^n$ for some different values of $n$ on Wolfram Alpha, to see what the book means.
– saulspatz
Jul 19 at 3:37
It means they don't grow very fast. Graph $y=x^n$ for some different values of $n$ on Wolfram Alpha, to see what the book means.
– saulspatz
Jul 19 at 3:37
zero of a polynomial function from book "Blitzer college algebra" Multiplicity and x-Intercepts If r is a zero of even multiplicity, then the graph touches the xaxis and turns around at r. If r is a zero of odd multiplicity, then the graph crosses the xaxis at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend to flatten out near zeros with multiplicity greater than one.
– Ahmed M. Elsonbaty
Jul 19 at 3:38
zero of a polynomial function from book "Blitzer college algebra" Multiplicity and x-Intercepts If r is a zero of even multiplicity, then the graph touches the xaxis and turns around at r. If r is a zero of odd multiplicity, then the graph crosses the xaxis at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend to flatten out near zeros with multiplicity greater than one.
– Ahmed M. Elsonbaty
Jul 19 at 3:38
@AhmedM.Elsonbaty Compare for example the "flatness" of $x, x^2, x^3, x^4$ around $,x=0,$.
– dxiv
Jul 19 at 4:10
@AhmedM.Elsonbaty Compare for example the "flatness" of $x, x^2, x^3, x^4$ around $,x=0,$.
– dxiv
Jul 19 at 4:10
add a comment |Â
1 Answer
1
active
oldest
votes
up vote
5
down vote
accepted
What the book is probably trying to convey is that when a polynomial has a repeated root, the slope of the function tends to approach zero when $y=0$. Take, for example, the graph of $y=left(x+1right)^3left(x+3right)$:
The graph has a repeated root of $x=-1$ with a multipicity of 3. The slope of the graph approaches zero as $x$ approaches -1.
answered Jul 19 at 3:42
csch2
220211
+1 for a crisp answer. In your last sentence you mean "slope of the tangent to the graph" I suppose.
– P Vanchinathan
Jul 19 at 3:51
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
5
down vote
accepted
What the book is probably trying to convey is that when a polynomial has a repeated root, the slope of the function tends to approach zero when $y=0$. Take, for example, the graph of $y=left(x+1right)^3left(x+3right)$:
The graph has a repeated root of $x=-1$ with a multipicity of 3. The slope of the graph approaches zero as $x$ approaches -1.
answered Jul 19 at 3:42
csch2
220211
+1 for a crisp answer. In your last sentence you mean "slope of the tangent to the graph" I suppose.
– P Vanchinathan
Jul 19 at 3:51
add a comment |Â
up vote
5
down vote
accepted
What the book is probably trying to convey is that when a polynomial has a repeated root, the slope of the function tends to approach zero when $y=0$. Take, for example, the graph of $y=left(x+1right)^3left(x+3right)$:
The graph has a repeated root of $x=-1$ with a multipicity of 3. The slope of the graph approaches zero as $x$ approaches -1.
answered Jul 19 at 3:42
csch2
220211
+1 for a crisp answer. In your last sentence you mean "slope of the tangent to the graph" I suppose.
– P Vanchinathan
Jul 19 at 3:51
add a comment |Â
up vote
5
down vote
accepted
up vote
5
down vote
accepted
What the book is probably trying to convey is that when a polynomial has a repeated root, the slope of the function tends to approach zero when $y=0$. Take, for example, the graph of $y=left(x+1right)^3left(x+3right)$:
The graph has a repeated root of $x=-1$ with a multipicity of 3. The slope of the graph approaches zero as $x$ approaches -1.
answered Jul 19 at 3:42
csch2
220211
What the book is probably trying to convey is that when a polynomial has a repeated root, the slope of the function tends to approach zero when $y=0$. Take, for example, the graph of $y=left(x+1right)^3left(x+3right)$:
The graph has a repeated root of $x=-1$ with a multipicity of 3. The slope of the graph approaches zero as $x$ approaches -1.
answered Jul 19 at 3:42
csch2
220211
answered Jul 19 at 3:42
csch2
220211
answered Jul 19 at 3:42
csch2
220211
answered Jul 19 at 3:42
csch2
220211
220211
+1 for a crisp answer. In your last sentence you mean "slope of the tangent to the graph" I suppose.
– P Vanchinathan
Jul 19 at 3:51
add a comment |Â
+1 for a crisp answer. In your last sentence you mean "slope of the tangent to the graph" I suppose.
– P Vanchinathan
Jul 19 at 3:51
+1 for a crisp answer. In your last sentence you mean "slope of the tangent to the graph" I suppose.
– P Vanchinathan
Jul 19 at 3:51
+1 for a crisp answer. In your last sentence you mean "slope of the tangent to the graph" I suppose.
– P Vanchinathan
Jul 19 at 3:51
add a comment |Â
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Could you give us a little more context? What book is it, and what is the subject? The "zero" of what?
– Suzet
Jul 19 at 3:36
1
It means they don't grow very fast. Graph $y=x^n$ for some different values of $n$ on Wolfram Alpha, to see what the book means.
– saulspatz
Jul 19 at 3:37
zero of a polynomial function from book "Blitzer college algebra" Multiplicity and x-Intercepts If r is a zero of even multiplicity, then the graph touches the xaxis and turns around at r. If r is a zero of odd multiplicity, then the graph crosses the xaxis at r. Regardless of whether the multiplicity of a zero is even or odd, graphs tend to flatten out near zeros with multiplicity greater than one.
– Ahmed M. Elsonbaty
Jul 19 at 3:38
@AhmedM.Elsonbaty Compare for example the "flatness" of $x, x^2, x^3, x^4$ around $,x=0,$.
– dxiv
Jul 19 at 4:10