Rose Harrison and Clara Huizink Solutions for Exercise 12: Practice 3

For pair of functions $f$ and $g$: $f\left(x\right)=1.5^x, g\left(x\right)=-1.5^x$

a. Describe each transformation(s) of function $f$ to function $g$.

b. Write $g$ in terms of $f$.

c. Sketch both the function on the same set of axes.

For pair of functions $f$ and $g$: $f\left(x\right)={\left(\frac{1}{2}\right)}^x, g\left(x\right)=2^x$

a. Describe each transformation(s) of function $f$ to function $g$.

b. Write $g$ in terms of $f$.

c. Sketch both the function on the same set of axes.

For pair of functions $f$ and $g$: $f\left(x\right)=3^x, g\left(x\right)=3^{x+2}-3$

a. Describe each transformation(s) of function $f$ to function $g$.

b. Write $g$ in terms of $f$.

c. Sketch both the function on the same set of axes.

For pair of functions $f$ and $g$: $f\left(x\right)=0.5^x, g\left(x\right)=0.5^{2x}$

a. Describe each transformation(s) of function $f$ to function $g$.

b. Write $g$ in terms of $f$.

c. Sketch both the function on the same set of axes.

For pair of functions $f$ and $g$: $f\left(x\right)=2^x, g\left(x\right)=2^{0.5x}$

a. Describe each transformation(s) of function $f$ to function $g$.

b. Write $g$ in terms of $f$.

c. Sketch both the function on the same set of axes.

For pair of functions $f$ and $g$: $f\left(x\right)={\left(\frac{1}{3}\right)}^x, g\left(x\right)=3\times {\left(\frac{1}{3}\right)}^x$

a. Describe each transformation(s) of function $f$ to function $g$.

b. Write $g$ in terms of $f$.

c. Sketch both the function on the same set of axes.

For pair of functions $f$ and $g$: $f\left(x\right)={\left(\frac{1}{2}\right)}^x, g\left(x\right)={\left(\frac{1}{2}\right)}^{-2x}$

a. Describe each transformation(s) of function $f$ to function $g$.

b. Write $g$ in terms of $f$.

c. Sketch both the function on the same set of axes.

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.

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