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The graph of
y=|x| is shifted down by 9 units.
What is the equation of the new graph?
Choose 1 answer:
(A)
y=|x|-9
(B)
y=|x+9|
(C)
y=|x|+9
(D)
y=|x-9|

The graph of $y=|x|$ is shifted down by $9$ units. $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x|-9$ $\newline$ (B) $y=|x+9|$ $\newline$ (C) $y=|x|+9$ $\newline$ (D) $y=|x-9|$

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Transformations of absolute value functions: translations, reflections, and dilations

Full solution

Q. The graph of

y=|x|

is shifted down by

9

units.

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=|x|-9

\newline

(B)

y=|x+9|

\newline

(C)

y=|x|+9

\newline

(D)

y=|x-9|

Understanding vertical shifting: Understand the effect of shifting a graph vertically. $\newline$ Shifting a graph down by $9$ units means that we subtract $9$ from the original $y$ -value of the function for every $x$ -value.
Applying vertical shift to the original function: Apply the vertical shift to the original function. $\newline$ The original function is $y = |x|$ . To shift it down by $9$ units, we subtract $9$ from the entire function. $\newline$ $y = |x| - 9$
Matching the transformed function with options: Match the transformed function with the given options. $\newline$ The transformed function $y = |x| - 9$ matches with option (A) $y = |x| - 9$ .

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