Question

vertical stretches and shrinks of exponential functions
which graph represents a function with a growth factor of \\(\frac{1}{2}\\)?

Explanation:

Step1: Recall growth factor definition

An exponential function with growth factor $b>1$ increases as $x$ increases, and has the form $y=a(b)^x$ where $b=2$ here. Functions with $0

Step2: Eliminate decay graphs

The top two graphs decrease as $x$ increases, so they represent decay (growth factor between 0 and 1), not growth.

Step3: Verify growth graph behavior

For $y=a(2)^x$, when $x$ increases by 1, $y$ doubles. The third graph (bottom of the visible growing graphs) shows increasing values that grow at a rate consistent with doubling, matching a growth factor of 2. The bottom-most graph appears to grow too slowly (likely a smaller growth factor or decay).

Answer:

The third graph (the lower of the two upward-sloping exponential curves, labeled with the top-most of the two bottom option markers)