Move the slider to $p=2$. This is the graph of $2f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,1\right)\rightarrow$$\left(-3,2\right)$
$\left(-1,-1\right)\rightarrow$
$\left(0,1\right)\rightarrow$
$\left(1,3\right)\rightarrow$
$\left(4,0\right)\rightarrow$
Move the slider to $p=3$. This is the graph of $3f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,1\right)\rightarrow$$\left(-3,3\right)$
$\left(-1,-1\right)\rightarrow$
$\left(0,1\right)\rightarrow$
$\left(2,2\right)\rightarrow$
$\left(4,0\right)\rightarrow$
Move the slider to $p=2$. This is the graph of $2f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,-12\right)\rightarrow$$\left(-3,-24\right)$
$\left(-2,0\right)\rightarrow$
$\left(-1,4\right)\rightarrow$
$\left(2,-2\right)\rightarrow$
$\left(4,9\right)\rightarrow$
Move the slider to $p=3$. This is the graph of $3f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,-12\right)\rightarrow$$\left(-3,-36\right)$
$\left(-1,4\right)\rightarrow$
$\left(1,0\right)\rightarrow$
$\left(2,-2\right)\rightarrow$
$\left(5,28\right)\rightarrow$
For the tranformation $f\left(x\right)\rightarrow pf\left(x\right)$, when $p\gt 1$, the graph of $f\left(x\right)$ is
with scale factor
.
The points move
the
-axis. This is also called a stretch or dilation with invariant
-axis.
Move the slider to $p=\frac{1}{2}$. This is the graph of $\frac{1}{2}f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,1\right)\rightarrow$$\left(-3,0.5\right)$
$\left(-2,2\right)\rightarrow$
$\left(-1,-1\right)\rightarrow$
$\left(1,3\right)\rightarrow$
$\left(4,0\right)\rightarrow$
Move the slider to $p=\frac{1}{4}$. This is the graph of $\frac{1}{4}f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,1\right)\rightarrow$$\left(-3,0.25\right)$
$\left(-2,2\right)\rightarrow$
$\left(-1,-1\right)\rightarrow$
$\left(1,3\right)\rightarrow$
$\left(4,0\right)\rightarrow$
Move the slider to $p=\frac{1}{2}$. This is the graph of $\frac{1}{2}f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,-12\right)\rightarrow$$\left(-3,-6\right)$
$\left(-2,0\right)\rightarrow$
$\left(-1,4\right)\rightarrow$
$\left(2,-2\right)\rightarrow$
$\left(5,28\right)\rightarrow$
For the tranformation $f\left(x\right)\rightarrow pf\left(x\right)$, when $0 \lt p\lt 1$, the graph of $f\left(x\right)$ is
with scale factor
.
The points move
the
-axis. This is also called a stretch or dilation with invariant
-axis.