Question

Select the correct answer.

Each statement describes a transformation of the graph of f(x)= root^3 x .Which statement correctly describes the graph of y= f(x - 7) + 3?
A. It is the graph of f translated 3 units up and 7 units to the left
B. It is the graph of f translated 7 units down and 3 units to the right.
C. It is the graph of f translated 7 units up and 3 units to the right.
D. It is the graph of f translated 3 units up and 7 units to the right

Answer 1

The correct transformation is a translation of the graph of f(x) to the right by 7 units and upward by 3 units. The correct statement is:

C. It is the graph of f translated 7 units to the right and 3 units up.

The function
`\( f(x) = \sqrt[3]{x} \)` represents the cube root function. Let's analyze the transformation described by y = f(x - 7) + 3.

In the given expression:

- The term (x - 7) inside the function represents a horizontal shift to the right by 7 units. This is because the function is replaced with f evaluated at (x - 7).

- The term +3 outside the function represents a vertical shift upward by 3 units.

Therefore, the correct transformation is a translation of the graph of f(x) to the right by 7 units and upward by 3 units. The correct statement is:

C. It is the graph of f translated 7 units to the right and 3 units up.

This indicates the correct direction and amount of translation for the given transformation.