The graph of y=|x| is reflected across the x-axis and then scaled vertically by a factor of (1)/(4). What is the equation of the new graph? Choose 1 answer: (A) y=-4|x| (B) y=|x|-4 (C) y=-(1)/(4)|x| (D) y=|x-4|

Reflect across x-axis: Reflect y=|x| across the x-axis. To reflect a graph across the x-axis, we multiply the function by -1. Reflected function: y = -|x|Scale vertically by 1/4: Scale the reflected function vertically by a factor of 1/4. To scale a function vertically, we multiply the function by the scaling factor. Scaled function: y = (1/4)(-|x|) = -(1/4)|x|

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The graph of
y=|x| is reflected across the
x-axis and then scaled vertically by a factor of
(1)/(4).
What is the equation of the new graph?
Choose 1 answer:
(A)
y=-4|x|
(B)
y=|x|-4
(C)
y=-(1)/(4)|x|
(D)
y=|x-4|

The graph of $y=|x|$ is reflected across the $x$ -axis and then scaled vertically by a factor of $\frac{1}{4}$ . $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=-4|x|$ $\newline$ (B) $y=|x|-4$ $\newline$ (C) $y=-\frac{1}{4}|x|$ $\newline$ (D) $y=|x-4|$

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Math Problems

Algebra 1

Transformations of absolute value functions: translations and reflections

Full solution

Q. The graph of

y=|x|

is reflected across the

x

-axis and then scaled vertically by a factor of

\frac{1}{4}

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=-4|x|

\newline

(B)

y=|x|-4

\newline

(C)

y=-\frac{1}{4}|x|

\newline

(D)

y=|x-4|

Reflect across x-axis: Reflect $y=|x|$ across the x-axis. $\newline$ To reflect a graph across the x-axis, we multiply the function by $-1$ . $\newline$ Reflected function: $y = -|x|$
Scale vertically by $\frac{1}{4}$ : Scale the reflected function vertically by a factor of $\frac{1}{4}$ . To scale a function vertically, we multiply the function by the scaling factor. Scaled function: $y = \left(\frac{\(1$}{$4$}\right)(-|x|) = -\left(\frac{$1$}{$4$}\right)|x|