Write the function g(x) which takes the function f(x)=3^x and shifts it to the right by 4 units, reflects it across the x-axis, and shifts it up 2 units

Question

Write the function g(x) which takes the function f(x)=3^x and shifts it to the right by 4 units, reflects it across the x-axis, and shifts it up 2 units.

I got y=3^-(x-3)+2 and i'm pretty sure that that's not completely correct.

Answer 1

PROBLEM

Write the function g(x) which takes the function f(x)=3^x and shifts it to the right by 4 units, reflects it across the x-axis, and shifts it up 2 units

Write the function g(x) which takes the function f(x)=3^x and shifts it to the right by 4 units, reflects it across the x-axis, and shifts it up 2 units.

I got y=3^-(x-3)+2 and i'm pretty sure that that's not completely correct.

Solution:

For the function f(x), g(x) = ±a[f(x - h)] + k, so for f(x) = 3^x, g(x) = -3^{(x - 4)} + 2

Representation of transformations:

1. Negative sign in front of 3 reflects function across the x-axis
2. (x - 4) translates function 4 units right
3. + 2 translates function 2 units up