Question

the graph of $y = |x|$ is reflected across the $x$-axis and then scaled vertically by a factor of $\frac{3}{8}$. what is the equation of the new graph? choose 1 answer: a $y = \frac{8}{3}|x|$ b $y = -\frac{8}{3}|x|$ c $y = \frac{3}{8}|x|$ d $y = -\frac{3}{8}|x|$

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 \( y=\vert x\vert \), after reflecting across the \( x \) - axis, the equation becomes \( y =-\vert x\vert \).

Step2: Vertically scale by factor \(\frac{3}{8}\)

To vertically scale a function \( y = f(x) \) by a factor of \( a \), we multiply the function by \( a \). Here, we have the function \( y =-\vert x\vert \) and we want to scale it vertically by a factor of \(\frac{3}{8}\). So we multiply \( -\vert x\vert \) by \(\frac{3}{8}\).
The new equation is \( y=-\frac{3}{8}\vert x\vert \)

Answer:

D. \( y = -\frac{3}{8}\vert x\vert \)