Question

the function $f(x) = x^3$ is stretched vertically, and the resulting function is $g(x) = af(x)$. identify which of the following values of $a$ could be responsible for this transformation. (1 point)

• 0.03
• 1.03
• 0.10
• 1

Explanation:

Step1: Recall Vertical Stretch Rule

For a function \( y = af(x) \), a vertical stretch occurs when \( |a|> 1 \). If \( 0 < |a| < 1 \), it's a vertical compression. If \( a = 1 \), there's no vertical transformation.

Step2: Analyze Each Option

• For \( a = 0.03 \): Since \( 0.03<1 \), this is a vertical compression, not a stretch.
• For \( a = 1.03 \): Since \( 1.03 > 1 \), this will vertically stretch the function \( f(x)=x^{3} \) to get \( g(x)=1.03x^{3} \).
• For \( a = 0.10 \): Since \( 0.10 < 1 \), this is a vertical compression, not a stretch.
• For \( a = 1 \): There is no vertical transformation (stretch or compression) as \( a = 1 \) leaves the function unchanged.

Answer:

1.03 (the option with value 1.03)