Question

The cube root function f(x)=³√x is changed to f(x)= 2.(³√x)-3. Which statement describes how the graph of f(x)=³√x will change?

A. The graph will shift to the left 3 units and will compress by a factor of 2
B. The graph will shift down 3 units and will stretch by a factor of 2
C. The graph will shift down 3 units and will compress by a factor of 2
D. The graph will shift to the left 3 units and will stretch by a factor of 2

Answer 1

The graph of f(x) = ³√x will shift down 3 units and compress by a factor of 2.

Step-by-step explanation:

The given function is f(x) = ³√x. The new function is f(x) = 2(³√x) - 3.

Let's analyze the changes to the original function:

• The factor 2 before the cube root compresses the graph horizontally by a factor of 2. This means the graph will be narrower.
• The exponent -3 after the cube root shifts the graph down by 3 units. This means the graph will be shifted downwards.

Therefore, the correct statement describing how the graph of f(x) = ³√x will change is C. The graph will shift down 3 units and will compress by a factor of 2.