The graph of y=|x| is shifted up by 7 units and to the left by 8 units. What is the equation of the new graph? Choose 1 answer: (A) y=|x+8|-7 (B) y=|x+8|+7 (C) y=|x-8|+7 (D) y=|x-8|-7

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 7 units adds 7 to the value of the function. A horizontal shift to the left by 8 units means we add 8 to the x-value inside the function before applying the absolute value.Applying Horizontal Shift: Let's apply the horizontal shift first. Shifting the graph to the left by 8 units means we replace x with (x+8) in the absolute value function. The new function becomes y = |x+8|.Applying Vertical Shift: Now, we apply the vertical shift. Shifting the graph up by 7 units means we add 7 to the entire function. So, the new function after both shifts is y = |x+8| + 7.Matching the Result: We can now match our result with the given choices. The correct equation after applying both shifts is y = |x+8| + 7, which corresponds to choice (B).

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The graph of
y=|x| is shifted up by 7 units and to the left by 8 units.
What is the equation of the new graph?
Choose 1 answer:
(A)
y=|x+8|-7
(B)
y=|x+8|+7
(C)
y=|x-8|+7
(D)
y=|x-8|-7

The graph of $y=|x|$ is shifted up by $7$ units and to the left by $8$ units. $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x+8|-7$ $\newline$ (B) $y=|x+8|+7$ $\newline$ (C) $y=|x-8|+7$ $\newline$ (D) $y=|x-8|-7$

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Math Problems

Algebra 2

Domain and range of absolute value functions: equations

Full solution

Q. The graph of

y=|x|

is shifted up by

7

units and to the left by

8

units.

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=|x+8|-7

\newline

(B)

y=|x+8|+7

\newline

(C)

y=|x-8|+7

\newline

(D)

y=|x-8|-7

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 $7$ units adds $7$ to the value of the function. A horizontal shift to the left by $8$ units means we add $8$ to the $x$ -value inside the function before applying the absolute value.
Applying Horizontal Shift: Let's apply the horizontal shift first. Shifting the graph to the left by $8$ units means we replace $x$ with $(x+8)$ in the absolute value function. The new function becomes $y = |x+8|$ .
Applying Vertical Shift: Now, we apply the vertical shift. Shifting the graph up by $7$ units means we add $7$ to the entire function. So, the new function after both shifts is $y = |x+8| + 7$ .
Matching the Result: We can now match our result with the given choices. The correct equation after applying both shifts is $y = |x+8| + 7$ , which corresponds to choice (B).