Question

Given the graph f(x)=4^x write a function that results from each given transformation. A. f(x)=4^x is shifted 4 units up. What is the equation of the new function?B. f(x)=4^x is shifted 3 units down. What is the equation of the new function?C. f(x)=4^x is shifted 2 units left. What is the equation of the new function?D. f(x)=4^x is shifted 5 units right. What is the equation of the new function?E. f(x)=4^x is reflected about the x-axis. What is the equation of the new function?F. f(x)=4^x is reflected about the y-axis. What is the equation of the new function?

Answer 1

Given:

There are given that the function:

$f(x)=4^x$

Explanation:

To find any transformation, we need to use the parent function which is given.

Then,

(A): Shifted 4 units up:

$\begin{gathered} f(x)=4^x \\ f(x)=4^x+4 \end{gathered}$

Hence, the new function is shown below:

$f(x)=4^x+4$

(B): Shifted 3 units down.

Then,

$\begin{gathered} f(x)=4^x \\ f(x)=4^x-3 \end{gathered}$

Hence, the new function is shown below:

$f(x)=4^x-3$

(C): Shifted 2 units left:

Then,

$\begin{gathered} f(x)=4^x \\ f(x)=4^{x+2} \end{gathered}$

Hence, the new function is shown below:

$f(x)=4^{x+2}$

(D): Shifted 5 units right.

$\begin{gathered} f(x)=4^x \\ f(x)=4^x-5 \end{gathered}$

Hence, the new function is shown below:

$f(x)=4^x-5$

(E); Reflected about x-axis:

$\begin{gathered} f(x)=4^x \\ f(x)=-4^x \end{gathered}$

Hence, the new function is shown below:

$f(x)=-4^x$

(F): Reflected about the y-axis:

Then,

$\begin{gathered} f(x)=4^x \\ f(x)=4^{(-x)}_{} \end{gathered}$

Hence, the new function is shown below:

$f(x)=4^{(-x)}_{}$