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(-4,12\right)\rightarrow$$\left(-4,24\right)$
$\left(-3,5\right)\rightarrow$
$\left(-2,0\right)\rightarrow$
$\left(0,-4\right)\rightarrow$
$\left(1,-3\right)\rightarrow$
Move the slider to $p=3$. This is the graph of $3f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,5\right)\rightarrow$$\left(-3,15\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,-4\right)\rightarrow$
$\left(1,-3\right)\rightarrow$
$\left(4,12\right)\rightarrow$
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(-4,12\right)\rightarrow$$\left(-4,6\right)$
$\left(-3,5\right)\rightarrow$
$\left(-2,0\right)\rightarrow$
$\left(0,-4\right)\rightarrow$
$\left(6,32\right)\rightarrow$
Move the slider to $p=\frac{1}{4}$. This is the graph of $\frac{1}{4}f\left(x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-4,-12\right)\rightarrow$$\left(-4,-3\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,-4\right)\rightarrow$
$\left(3,5\right)\rightarrow$
$\left(5,25\right)\rightarrow$
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.