Question

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

Explanation:

Step1: Recall vertical stretch rule

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

Step2: Evaluate given $a$ values

Check each option:

• $1.0$: $|1.0|=1$ (no stretch/shrink)
• $0.9$: $|0.9|<1$ (vertical shrink)
• $1.5$: $|1.5|>1$ (vertical stretch)
• $0.3$: $|0.3|<1$ (vertical shrink)

Answer:

1.5