Question
Which of the following correctly identifies how \( h(x)=2 x^{3} \) compares to its parent function? (1 point) \( h(x) \) 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. \( h(x) \) 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.
Ask by Wyatt Munoz. in the United States
Jan 23,2025
Real Tutor Solution
Tutor-Verified Answer
Answer
\( h(x) \) is the result of the cubic parent function being vertically stretched.
Solution
The function \( h(x) = 2x^3 \) is a transformation of the parent cubic function \( f(x) = x^3 \).
When a function is multiplied by a constant greater than 1, it results in a **vertical stretch**. In this case, the factor is 2, which means the graph of \( h(x) \) is stretched vertically by a factor of 2 compared to the parent function.
**Correct Answer:**
\( h(x) \) is the result of the cubic parent function being vertically stretched.
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Simplify this solution Mind Expander
The function \( h(x) = 2x^3 \) can be seen as a vertical stretch of the cubic parent function \( f(x) = x^3 \). The coefficient \( 2 \) multiplies the output values of the basic cubic function, causing the graph to stretch away from the x-axis. As a result, points on the graph will rise (or fall) more steeply than they would under the parent function. In contextual terms, think of it like a rubber band! When you pull the rubber band (which represents the basic cubic function) further away from the center (the x-axis), it becomes stretched and amplifies its movement. So every point on \( h(x) \) reaches new heights (or depths) compared to its more mellow parent function.
