Question

Suppose that F(x) = x2 and G(x) = -1/3(x+4)2. Which statement best compares the graph of G(x) with the graph of F(x)

Answer 1

Compress the graph

Flip the graph

Shift the graph 4 units to the left

Explanation:

When functions are transformed there are a few simple rules:

• Adding/subtracting inside the parenthesis to the input shifts the function left(+) and right(-).
• Adding/subtracting outside the parenthesis to the output shifts the function up(+) and down(-).
• Multiplying the function by a number less than 1 compresses it towards the x-axis.
• Multiplying the function by a number greater than 1 stretches it away from the x-axis.

This graph has been multiplied by -1/3 which is less than 1. It will be compressed.

It will also flip the graph since it is changing to a negative and be an upside down U.

This graph has x added to by 4. It will shift left 4 units.