Question

For an unknown parent function f(x), write a function g(x) that is:-vertically stretched by a factor of 2,- shifted up 5 units, and - shifted right 4 units. Explain how your function accomplishes these transformations.

Answer 1

Given the parent function to be:

`f(x)`

Write the function g(x), when the parent function is

1. vertically stretched by a factor of 2 - Multiply the parent function by 2

`g(x)=2f(x)`

2. Shifted up 5 units - Add 5 units outside of the parent function

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

3. Shifted right 4 units - Subtract 4 from within the parent function

`g(x)=2f(x-4)+5`

Therefore, the transformation of the parent function f(x) to g(x) is

`g(x)=2f(x-4)+5`