Question

scaling the cubic function quick check
which of the following correctly identifies how $h(x) = 2x^3$ compares to its parent function? (1 point)

• $h(x)$ is the result of the cubic parent function being vertically translated down.
• $h(x)$ is the result of the cubic parent function being vertically compressed.
• $h(x)$ is the result of the cubic parent function being vertically translated up.
• $h(x)$ is the result of the cubic parent function being vertically stretched.

Explanation:

Step1: Recall Parent Function

The parent function of \( h(x) = 2x^3 \) is \( f(x)=x^3 \).

Step2: Analyze Transformation

For a function \( y = a\cdot f(x) \), if \( |a|>1 \), it's a vertical stretch; if \( 0<|a|<1 \), it's a vertical compression. Here, \( a = 2 \) (and \( |2|>1 \)), so \( h(x) = 2x^3 \) is a vertical stretch of \( f(x)=x^3 \). The other options (translations) involve adding/subtracting constants, not multiplying by a constant greater than 1.

Answer:

\( h(x) \) is the result of the cubic parent function being vertically stretched. (The option: \( h(x) \) is the result of the cubic parent function being vertically stretched.)