Given:
There are given that the function:
[tex]f(x)=4^x[/tex]Explanation:
To find any transformation, we need to use the parent function which is given.
Then,
(A): Shifted 4 units up:
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^x+4 \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^x+4[/tex](B): Shifted 3 units down.
Then,
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^x-3 \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^x-3[/tex](C): Shifted 2 units left:
Then,
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^{x+2} \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^{x+2}[/tex](D): Shifted 5 units right.
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^x-5 \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^x-5[/tex](E); Reflected about x-axis:
[tex]\begin{gathered} f(x)=4^x \\ f(x)=-4^x \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=-4^x[/tex](F): Reflected about the y-axis:
Then,
[tex]\begin{gathered} f(x)=4^x \\ f(x)=4^{(-x)}_{} \end{gathered}[/tex]Hence, the new function is shown below:
[tex]f(x)=4^{(-x)}_{}[/tex]
