question on plotting graph
if we have the set of all ordered pairs $(x,x^2/y)$ such that x is inn $R$ an y is in $N$ then am I right in saying this is like the set of ordered pairs defined by $y=x^2$ and also $y=(1/2)x^2$ and so on so to plot this set on the x-y plane it would look like y=x^2 and then lots of the same stretched by scale factor 1/2 in the y direction?
Thanks
graphing-functions
asked Nov 26 at 22:35
Johnf
153
add a comment |
if we have the set of all ordered pairs $(x,x^2/y)$ such that x is inn $R$ an y is in $N$ then am I right in saying this is like the set of ordered pairs defined by $y=x^2$ and also $y=(1/2)x^2$ and so on so to plot this set on the x-y plane it would look like y=x^2 and then lots of the same stretched by scale factor 1/2 in the y direction?
Thanks
graphing-functions
asked Nov 26 at 22:35
Johnf
153
add a comment |
if we have the set of all ordered pairs $(x,x^2/y)$ such that x is inn $R$ an y is in $N$ then am I right in saying this is like the set of ordered pairs defined by $y=x^2$ and also $y=(1/2)x^2$ and so on so to plot this set on the x-y plane it would look like y=x^2 and then lots of the same stretched by scale factor 1/2 in the y direction?
Thanks
graphing-functions
asked Nov 26 at 22:35
Johnf
153
if we have the set of all ordered pairs $(x,x^2/y)$ such that x is inn $R$ an y is in $N$ then am I right in saying this is like the set of ordered pairs defined by $y=x^2$ and also $y=(1/2)x^2$ and so on so to plot this set on the x-y plane it would look like y=x^2 and then lots of the same stretched by scale factor 1/2 in the y direction?
Thanks
graphing-functions
graphing-functions
asked Nov 26 at 22:35
Johnf
153
asked Nov 26 at 22:35
Johnf
153
asked Nov 26 at 22:35
Johnf
153
asked Nov 26 at 22:35
Johnf
153
asked Nov 26 at 22:35
Johnf
153
153
add a comment |
add a comment |
2 Answers
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You are entirely correct, the set of the ordered pairs you describe is the union of the graphs of the functions $f_y: mathbb{R} to mathbb{R}_+, x mapsto frac{x^2}{y}$ for $y in mathbb{N}$.
Here's a quick plot to support your intuition.
You should perhaps avoid saying the pairs are defined by $y = x^2$ though, as your parameter is already called $y$ and it might lead to confusion. Using my notation from above and describing the pairs in the form $(x,f_y(x))$ will be more practical if you need to work with them further.
answered Nov 26 at 22:57
DC2K
163
add a comment |
Yes, the graph of the ordered pairs $(x,x^2/n)$ is the graph of $y=x^2/n$. It's graph would be like the graph of $y=x^2$ but shrunk by a factor of $1/n$ vertically. If $n$ is negative, it will also be reflected in the $x$-axis.
answered Nov 26 at 22:57
John Wayland Bales
13.8k21137
add a comment |
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2 Answers
2
active
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2 Answers
2
active
oldest
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active
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You are entirely correct, the set of the ordered pairs you describe is the union of the graphs of the functions $f_y: mathbb{R} to mathbb{R}_+, x mapsto frac{x^2}{y}$ for $y in mathbb{N}$.
Here's a quick plot to support your intuition.
You should perhaps avoid saying the pairs are defined by $y = x^2$ though, as your parameter is already called $y$ and it might lead to confusion. Using my notation from above and describing the pairs in the form $(x,f_y(x))$ will be more practical if you need to work with them further.
answered Nov 26 at 22:57
DC2K
163
add a comment |
You are entirely correct, the set of the ordered pairs you describe is the union of the graphs of the functions $f_y: mathbb{R} to mathbb{R}_+, x mapsto frac{x^2}{y}$ for $y in mathbb{N}$.
Here's a quick plot to support your intuition.
You should perhaps avoid saying the pairs are defined by $y = x^2$ though, as your parameter is already called $y$ and it might lead to confusion. Using my notation from above and describing the pairs in the form $(x,f_y(x))$ will be more practical if you need to work with them further.
answered Nov 26 at 22:57
DC2K
163
add a comment |
You are entirely correct, the set of the ordered pairs you describe is the union of the graphs of the functions $f_y: mathbb{R} to mathbb{R}_+, x mapsto frac{x^2}{y}$ for $y in mathbb{N}$.
Here's a quick plot to support your intuition.
You should perhaps avoid saying the pairs are defined by $y = x^2$ though, as your parameter is already called $y$ and it might lead to confusion. Using my notation from above and describing the pairs in the form $(x,f_y(x))$ will be more practical if you need to work with them further.
answered Nov 26 at 22:57
DC2K
163
You are entirely correct, the set of the ordered pairs you describe is the union of the graphs of the functions $f_y: mathbb{R} to mathbb{R}_+, x mapsto frac{x^2}{y}$ for $y in mathbb{N}$.
Here's a quick plot to support your intuition.
You should perhaps avoid saying the pairs are defined by $y = x^2$ though, as your parameter is already called $y$ and it might lead to confusion. Using my notation from above and describing the pairs in the form $(x,f_y(x))$ will be more practical if you need to work with them further.
answered Nov 26 at 22:57
DC2K
163
answered Nov 26 at 22:57
DC2K
163
answered Nov 26 at 22:57
DC2K
163
answered Nov 26 at 22:57
DC2K
163
163
add a comment |
add a comment |
Yes, the graph of the ordered pairs $(x,x^2/n)$ is the graph of $y=x^2/n$. It's graph would be like the graph of $y=x^2$ but shrunk by a factor of $1/n$ vertically. If $n$ is negative, it will also be reflected in the $x$-axis.
answered Nov 26 at 22:57
John Wayland Bales
13.8k21137
add a comment |
Yes, the graph of the ordered pairs $(x,x^2/n)$ is the graph of $y=x^2/n$. It's graph would be like the graph of $y=x^2$ but shrunk by a factor of $1/n$ vertically. If $n$ is negative, it will also be reflected in the $x$-axis.
answered Nov 26 at 22:57
John Wayland Bales
13.8k21137
add a comment |
Yes, the graph of the ordered pairs $(x,x^2/n)$ is the graph of $y=x^2/n$. It's graph would be like the graph of $y=x^2$ but shrunk by a factor of $1/n$ vertically. If $n$ is negative, it will also be reflected in the $x$-axis.
answered Nov 26 at 22:57
John Wayland Bales
13.8k21137
Yes, the graph of the ordered pairs $(x,x^2/n)$ is the graph of $y=x^2/n$. It's graph would be like the graph of $y=x^2$ but shrunk by a factor of $1/n$ vertically. If $n$ is negative, it will also be reflected in the $x$-axis.
answered Nov 26 at 22:57
John Wayland Bales
13.8k21137
answered Nov 26 at 22:57
John Wayland Bales
13.8k21137
answered Nov 26 at 22:57
John Wayland Bales
13.8k21137
answered Nov 26 at 22:57
John Wayland Bales
13.8k21137
13.8k21137
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add a comment |
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