Question

Suppose that G(X) = F(x+ 9). Which statement best compares the graph of

G(x) with the graph of f(x)?

Answer 1

D. The graph of G(x) is the graph of F(x) shifted 9 units to the left.

EXPLANATION

The given functions are F(x) and G(x).

The function, G(x) is obtain by translating or shifting the graph of F(x).

This translation is of the form.

`G(x) = F(x+ 9)`

The '+9' within the parenthesis tells us that the shift is 9 units to the left.

Remember that for horizontal shift:

+ means a shift to the left.

The correct answer is D.

Answer 2

Answer: Option D

Explanation:

By definition if we have a function F (x) and perform a transformation of the form

`G (x) = F (x + c)`

Then it is true that:

If c is negative the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the right

If c is positive, the graph of G(x) will be equal to the graph of F(x) displaced horizontally c units to the left.

Note that in this case the transformation is:

`G (x) = F (x + 9)`

Then
`c = 9` and
`c> 0`

Therefore the graph of G(x) will be equal to the graph of F(x) displaced horizontally 9 units to the left

The answer is the option D.