Question

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

Explanation:

Step1: Recall vertical stretch rule

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

Step2: Evaluate given $a$ values

Check which $a$ satisfies $a>1$:

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

Answer:

1.5