The graph of $y=|x|$ is reflected across the $x$ -axis and then scaled vertically by a factor of $\frac{3}{8}$ . $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=\frac{8}{3}|x|$ $\newline$ (B) $y=-\frac{8}{3}|x|$ $\newline$ (C) $y=\frac{3}{8}|x|$ $\newline$ (D) $y=-\frac{3}{8}|x|$

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Algebra 2

Domain and range of absolute value functions: equations

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Q. The graph of

y=|x|

is reflected across the

x

-axis and then scaled vertically by a factor of

\frac{3}{8}

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=\frac{8}{3}|x|

\newline

(B)

y=-\frac{8}{3}|x|

\newline

(C)

y=\frac{3}{8}|x|

\newline

(D)

y=-\frac{3}{8}|x|

Reflection across x-axis: Reflecting the graph of $y = |x|$ across the x-axis means we need to multiply the function by $-1$ , because reflection across the x-axis changes the sign of the $y$ -values.
Scaling vertically by $\frac{3}{8}$ : The reflection of $y = |x|$ across the $x$ -axis is $y = -|x|$ .
Final equation after transformations: Next, we need to scale the reflected graph vertically by a factor of $\frac{3}{8}$ . This means we multiply the entire function by $\frac{3}{8}$ .
Final equation after transformations: Next, we need to scale the reflected graph vertically by a factor of $\frac{3}{8}$ . This means we multiply the entire function by $\frac{3}{8}$ .Scaling $y = -|x|$ by a factor of $\frac{3}{8}$ gives us the new function $y = \left(\frac{3}{8}\right)(-|x|)$ .
Final equation after transformations: Next, we need to scale the reflected graph vertically by a factor of $\frac{3}{8}$ . This means we multiply the entire function by $\frac{3}{8}$ . Scaling $y = -|x|$ by a factor of $\frac{3}{8}$ gives us the new function $y = \left(\frac{3}{8}\right)(-|x|)$ . Simplify the expression to get the final equation of the new graph. Multiplying $-1$ by $\frac{3}{8}$ gives us $-\frac{3}{8}$ .
Final equation after transformations: Next, we need to scale the reflected graph vertically by a factor of $\frac{3}{8}$ . This means we multiply the entire function by $\frac{3}{8}$ .Scaling $y = -|x|$ by a factor of $\frac{3}{8}$ gives us the new function $y = \left(\frac{3}{8}\right)(-|x|)$ .Simplify the expression to get the final equation of the new graph. Multiplying $-1$ by $\frac{3}{8}$ gives us $-\frac{3}{8}$ .The final equation of the new graph after the transformations is $y = -\left(\frac{3}{8}\right)|x|$ .