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The graph of
y=|x| is shifted up by 4 units and to the right by 5 units.
What is the equation of the new graph?
Choose 1 answer:
(A)
y=|x+4|-5
(B)
y=|x+5|+4
(C)
y=|x-5|+4
(D)
y=|x+4|+5

The graph of $y=|x|$ is shifted up by $4$ units and to the right by $5$ units. $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x+4|-5$ $\newline$ (B) $y=|x+5|+4$ $\newline$ (C) $y=|x-5|+4$ $\newline$ (D) $y=|x+4|+5$

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Domain and range of absolute value functions: equations

Full solution

Q. The graph of

y=|x|

is shifted up by

4

units and to the right by

5

units.

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=|x+4|-5

\newline

(B)

y=|x+5|+4

\newline

(C)

y=|x-5|+4

\newline

(D)

y=|x+4|+5

Understanding shifts: To determine the equation of the transformed graph, we need to understand how shifts affect the equation of a function. A vertical shift up by $4$ units adds $4$ to the value of $y$ in the original equation. A horizontal shift to the right by $5$ units subtracts $5$ from the value of $x$ in the original equation.
Vertical shift up: The original equation is $y = |x|$ . To shift the graph up by $4$ units, we add $4$ to the $y$ -value, resulting in $y = |x| + 4$ .
Horizontal shift to the right: To shift the graph to the right by $5$ units, we subtract $5$ from the $x$ -value inside the absolute value, resulting in $y = |x - 5| + 4$ .
Comparing transformed equation: Now we compare the transformed equation with the given choices to find the correct answer. $\newline$ (A) $y = |x + 4| - 5$ is incorrect because it represents a shift to the left by $4$ units and down by $5$ units. $\newline$ (B) $y = |x + 5| + 4$ is incorrect because it represents a shift to the left by $5$ units and up by $4$ units. $\newline$ (C) $y = |x - 5| + 4$ is correct because it represents a shift to the right by $5$ units and up by $4$ units. $\newline$ (D) $y = |x + 4| + 5$ is incorrect because it represents a shift to the left by $4$ units and up by $5$ units.

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