Question

7. Write an equation that results when f(x) = 5^x has been transformed by:a. Shifted to the left 2 and up 3b. Shifted right 3 and down 1

Answer 1

`\begin{gathered} (a)g(x)=5^(x+2)+3 \\ (b)g(x)=5^(x-3)-1 \end{gathered}`

Step-by-step explanation:

Given the parent function f(x) defined below:

`f\mleft(x\mright)=5^x`

Part A

When f(x) is shifted to the left 2 units:

`f(x+2)=5^(x+2)`

Next, shifted up by 3 units:

`f(x+2)+3=5^(x+2)+3`

The result is:

`g(x)=5^(x+2)+3`

Part B

When f(x) is shifted to the right 3 units:

`f(x-3)=5^(x-3)`

Next, shifted down by 1 unit:

`f(x-3)-1=5^(x-3)-1`

The result is:

`g(x)=5^(x-3)-1`