Question

the graph of $y = |x|$ is reflected across the $x$-axis and then scaled vertically by a factor of $\frac{1}{4}$. what is the equation of the new graph? choose 1 answer: a $y = -4|x|$ b $y = |x| - 4$ c $y = -\frac{1}{4}|x|$ d $y = |x - 4|$

Explanation:

Step1: Reflect across x - axis

To reflect a function \( y = f(x) \) across the \( x \) - axis, we replace \( y \) with \( -y \). For the function \( y=|x| \), after reflecting across the \( x \) - axis, the equation becomes \( y=-|x| \).

Step2: Vertically scale by \( \frac{1}{4} \)

To vertically scale a function \( y = f(x) \) by a factor of \( a \), we multiply the function by \( a \). Here, we want to vertically scale \( y = -|x| \) by a factor of \( \frac{1}{4} \). So we multiply \( -|x| \) by \( \frac{1}{4} \), and we get \( y=-\frac{1}{4}|x| \).

Answer:

C. \( y = -\frac{1}{4}|x| \)