Question

What exponential function, g(x), will translate the original function, = 3.5^ − 4, 4 units to the right and 6 units up?

Answer 1

Given:

$f(x)=3.5^x-4$

Required:

We need to find the function g(x) that translates the function f(x) 4 units right and 6 units up.

Explanation:

In the exponential function f(x-4) shift the function f(x) 4 units right,

Replace x = x-4 in the given function f(x).

$f(x-4)=3.5^{x-4}-4$

Add 6 to both sides of the equation to life the function f(x) up by 6 units.

$f(x-4)+6=3.5^{x-4}-4+6$$f(x-4)+6=3.5^{x-4}+2$

$Let\text{ }g(x)=f(x-4)+6.$

We get

$g(x)=3.5^{x-4}+2$

Final answer:

$g(x)=3.5^{x-4}+2$