Question

Which transformations have been performed on the graph of f(x) =
`\sqrt[3]{x}` to obtain the graph g(x) = 1/4
`\sqrt[3]{x+3}` + 6

Select each correct answer.



(A) reflect the graph over the x-axis

(B) compress the graph closer to the x-axis

(C) translate the graph down

(D) translate the graph to the right

(E) translate the graph to the left

(F) translate the graph up

(G) stretch the graph away from the x-axis

Answer 1

(B) compress the graph closer to the x-axis

(E) translate the graph to the left

(F) translate the graph up

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 1/4 which is less than 1. It will be compressed.

This graph has x added to by 3. It will shift left 3 units.

This graph has the output outside of x added to by 6. It will shift 6 units up. See picture below. The original function is red. The new function is blue.