Question

Suppose that G(x) = F(x-2)+7. Which statement best compares the graph of G(x) with the graph of F(x)?

Answer 1

g(x) is f(x) shifted 2 units right and 7 units up

Explanation:

Given

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

Required

Relationship between f(x) and g(x)

We have:

`f(x)`

When f(x) is shifted 2 units to the right;

The rule is:

`x \to x -2`

So, it becomes:

`f(x - 2)`

When
`f(x - 2)` is shifted up by 7 units,

The rule is:

`y \to y + 7`

So, it becomes:

`f(x - 2) + 7`

Hence;

g(x) is f(x) shifted 2 units right and 7 units up