Question

graphing the cube root function using the graph of $f(x) = \sqrt3{x}$, decide which of the statements is true. statement #1: $f(2) = -8$ statement #2: $f(-8) = 2$ statement #3: $f(2) = 8$ statement #4: $f(8) = 2$ (1 point)

Explanation:

Step1: Recall the cube root function

The function is \( f(x)=\sqrt[3]{x} \). We need to check each statement by calculating \( f(x) \) for the given \( x \).

Step2: Check Statement #1

For \( f(2) \), calculate \( \sqrt[3]{2} \approx 1.26 \), not \(-8\). So Statement #1 is false.

Step3: Check Statement #2

For \( f(-8) \), calculate \( \sqrt[3]{-8}=-2 \), not \( 2 \). So Statement #2 is false.

Step4: Check Statement #3

For \( f(2) \), as in Step2, \( \sqrt[3]{2}\approx1.26 \), not \( 8 \). So Statement #3 is false.

Step5: Check Statement #4

For \( f(8) \), calculate \( \sqrt[3]{8} = 2 \) (since \( 2^3 = 8 \)). So Statement #4 is true.

Answer:

Statement #4: \( f(8) = 2 \) (i.e., the statement \( f(8) = 2 \) is true)