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.

Step-by-step 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`