Question

Let f(x)=−2x−7. Write a function g whose graph is a translation 6 units to the right of the graph of f

Answer 1

`y=-2x+5`

Explanation:

Translation of a Graph

If the graph of y=f(x) is translated a units horizontally and b units vertically, then the equation of the translated graph is :

`y -b=f(x - a)`

The function given in the question is

`f(x)=-2x-7`

We are required to translate it 6 units to the right, or a=6. No vertical translation is required, thus, the function whose graph is 6 units translated to the right is:

`y=-2(x-6)-7`

Operating:

`y=-2x+12-7`

`\boxed{y=-2x+5}`