Answer:
[tex]\begin{gathered} (a)g(x)=5^{x+2}+3 \\ (b)g(x)=5^{x-3}-1 \end{gathered}[/tex]Explanation:
Given the parent function f(x) defined below:
[tex]f\mleft(x\mright)=5^x[/tex]Part A
When f(x) is shifted to the left 2 units:
[tex]f(x+2)=5^{x+2}[/tex]Next, shifted up by 3 units:
[tex]f(x+2)+3=5^{x+2}+3[/tex]The result is:
[tex]g(x)=5^{x+2}+3[/tex]Part B
When f(x) is shifted to the right 3 units:
[tex]f(x-3)=5^{x-3}[/tex]Next, shifted down by 1 unit:
[tex]f(x-3)-1=5^{x-3}-1[/tex]The result is:
[tex]g(x)=5^{x-3}-1[/tex]