Question

which of the following exponential equations shows a horizontal stretch of the function $y = 7^{x}$? (5 points)○ $y = \frac{1}{2} \cdot 7^{x}$○ $y = 7^{\frac{1}{2}x}$○ $y = 2 \cdot 7^{x}$○ $y = 7^{2x}$

Explanation:

Step1: Recall horizontal stretch rule

For a function $y = f(x)$, a horizontal stretch by factor $\frac{1}{k}$ is $y = f(kx)$ where $0 < k < 1$.

Step2: Analyze each option

• $y=\frac{1}{2}\cdot7^x$: Vertical compression, not horizontal stretch.
• $y=7^{\frac{1}{3}x}$: Matches $f(kx)$ with $k=\frac{1}{3}$ (0<k<1), horizontal stretch.
• $y=2\cdot7^x$: Vertical stretch, not horizontal stretch.
• $y=7^{2x}$: Horizontal compression, not stretch.

Answer:

$y = 7^{\frac{1}{3}x}$