Question

which value of a in the exponential function would cause the function to stretch?
f(x) = a(\frac{1}{3})^x
1.5
1.0
0.3
0.9

Explanation:

Step1: Recall Stretch Rule

For exponential function \( f(x) = a(b)^x \), vertical stretch occurs when \( |a| > 1 \).

Step2: Evaluate Options

• \( 1.5 \): \( |1.5| > 1 \) (stretch candidate).
• \( 1.0 \): \( |1.0| = 1 \) (no stretch, just vertical shift/identity).
• \( 0.3 \): \( |0.3| < 1 \) (compression).
• \( 0.9 \): \( |0.9| < 1 \) (compression).

Answer:

1.5