Question

When equation represents the function f(x)=(1.6)x after it has been translated 5 units up 9 units to the right?

Answer 1

For this question my answer would be

g(x)=(1.6)x-9+5

Hope this Helps

Answer 2

`g(x)=(1.6)^(x-9)+5`

Explanation:

Given:
`f(x)=(1.6)^x`

The given function is
`f(x)=(1.6)^x`.

It is exponential function because x as power of 1.6.

For left / right shift : change in x value

• For right
  `x\rightarrow x-a`
• For left
  `x\rightarrow x+a`

For up / down shift : change in f(x)

• For up
  `f(x)\rightarrow f(x)+a`
• For down
  `f(x)\rightarrow f(x)-a`

`f(x)=(1.6)^x`

Shift up 5 units

`g(x)=f(x)+5`

Shift 9 unit right

`g(x)=f(x-9)+5`

`g(x)=1.6^(x-9)+5`

Hence, The new function will be
`g(x)=(1.6)^(x-9)+5`