Question

the graph of $y = |x|$ is reflected across the $x$-axis and then scaled vertically by a factor of 7.
what is the equation of the new graph?
choose 1 answer:
a $y = 7|x|$
b $y = -7|x|$
c $y = \frac{1}{7}|x|$
d $y = -\frac{1}{7}|x|$

Explanation:

Step1: Reflect over x-axis

To reflect $y=|x|$ across the x-axis, multiply the entire function by $-1$:
$y = -|x|$

Step2: Vertical scale by factor 7

To vertically scale the function by a factor of 7, multiply the function by 7:
$y = 7(-|x|) = -7|x|$

Answer:

B. $y = -7|x|$