Question

write a formula for the function $h(x)$ that relates to when the graph of a basic function is transformed as described. the graph of $g(x) = \sqrt{x}$ reflected over the $x$-axis and horizontally stretched by a factor of 5. select one: a. $h(x) = \sqrt{5x}$ b. $h(x) = -\sqrt{5x}$ c. $h(x) = \sqrt{-5x}$ d. $h(x) = -\sqrt{\frac{1}{5}x}$

Explanation:

Step1: Reflect over x-axis

To reflect $g(x)=\sqrt{x}$ over the x-axis, multiply the function by $-1$:
$g_1(x) = -\sqrt{x}$

Step2: Horizontal stretch by factor 5

For a horizontal stretch by factor $k$, replace $x$ with $\frac{x}{k}$. Here $k=5$, so substitute $x$ with $\frac{x}{5}$:
$h(x) = -\sqrt{\frac{1}{5}x}$

Answer:

D. $h(x) = -\sqrt{\frac{1}{5}x}$