Rose Harrison and Clara Huizink Solutions for Exercise 16: Mixed practice

Write the transformation in terms of the $f\left(x\right)=2^x$ when $f$ is reflected in the $y-$axis.

Write the transformation in terms of the $f\left(x\right)=2^x$ when $f$ translated $3$ units to the left and $4$ units down.

Write the transformation in terms of the $f\left(x\right)=2^x$ when $f$ is reflected in the $x-$axis.

Write the transformation in terms of the $f\left(x\right)=2^x$ when $f$ is dilated by scale factor $3$ parallel to $x-$axis.

Write the transformation in terms of the $f\left(x\right)=2^x$ when $f$ is dilated by scale factor $4$ parallel to $y-$axis.

On the same set of axes, sketch the graph of the function $f$ and its three transformations, Label each graph and any intercepts with the axes.

$f\left(x\right)=4^x; f_1\left(x\right)=4^{2x}; f_2\left(x\right)=-2\times 4^{0.5x}; f_3\left(x\right)=\frac{1}{2}\times 4^{-2x}$

Rewrite the function $f\left(x\right)=9^x$ with a base of $3$ instead of $9$. Then describe how you can graph this function using the base of $3$, in the form $y=3^{ax}$.

Rewrite the function $f\left(x\right)=9^x$ with a base of $81$. Then describe how you can graph this function using $81$ as a base, in the form $y={81}^{ax}$.