Move the slider to $q=2$. This is the graph of $f\left(2x\right)$ 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$$\left(-2,12\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,-4\right)\rightarrow$
$\left(3,5\right)\rightarrow$
$\left(6,32\right)\rightarrow$
Move the slider to $q=4$. This is the graph of $f\left(4x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-4,12\right)\rightarrow$$\left(-1,12\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,-4\right)\rightarrow$
$\left(3,5\right)\rightarrow$
$\left(8,60\right)\rightarrow$
Move the slider to $q=2$. This is the graph of $f\left(2x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-4,-35\right)\rightarrow$$\left(-2,-35\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,3\right)\rightarrow$
$\left(2,-2\right)\rightarrow$
$\left(5,28\right)\rightarrow$
Move the slider to $q=4$. This is the graph of $f\left(4x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-4,-35\right)\rightarrow$$\left(-1,-35\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,3\right)\rightarrow$
$\left(3,0\right)\rightarrow$
$\left(6,60\right)\rightarrow$
For the tranformation $f\left(x\right)\rightarrow f\left(qx\right)$, when $q\gt 1$, 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 $q=\frac{1}{2}$. This is the graph of $f\left(\frac{1}{2}x\right)$ 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$$\left(-8,12\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,-4\right)\rightarrow$
$\left(3,5\right)\rightarrow$
$\left(7,45\right)\rightarrow$
Move the slider to $q=\frac{1}{4}$. This is the graph of $f\left(\frac{1}{4}x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,5\right)\rightarrow$$\left(-12,5\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,-4\right)\rightarrow$
$\left(3,5\right)\rightarrow$
$\left(4,12\right)\rightarrow$
Move the slider to $q=\frac{1}{2}$. This is the graph of $f\left(\frac{1}{2}x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-4,-35\right)\rightarrow$$\left(-8,-35\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,3\right)\rightarrow$
$\left(3,0\right)\rightarrow$
$\left(6,60\right)\rightarrow$
Move the slider to $q=\frac{1}{4}$. This is the graph of $f\left(\frac{1}{4}x\right)$ where $f\left(x\right)$ is the original function.
Write down the new coordinates of the following points. For example $\left(-3,-12\right)\rightarrow$$\left(-12,-12\right)$
$\left(-2,0\right)\rightarrow$
$\left(0,3\right)\rightarrow$
$\left(2,-2\right)\rightarrow$
$\left(4,9\right)\rightarrow$
For the tranformation $f\left(x\right)\rightarrow f\left(qx\right)$, when $0 \lt q\lt 1$, 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.