The graph of y=|x| is shifted to the left by 6 units. What is the equation of the new graph? Choose 1 answer: (A) y=|x+6|-6 (B) y=|x-6|-6 (C) y=|x|-6 (D) y=|x+6|

Replace with (x + 6): To shift the graph of y=|x| to the left by 6 units, we need to replace x with (x + 6) in the equation. The transformation rule for horizontal shifts is: if a graph y=f(x) is shifted to the left by k units, the new graph will be y=f(x+k).Apply transformation rule: Apply the transformation rule to the given function y=|x|. The new equation after shifting to the left by 6 units will be y=|x+6|.Check answer choices: Check the answer choices to see which one matches the transformed equation. (A) y=|x+6|-6 (Incorrect, this represents a shift left and down) (B) y=|x-6|-6 (Incorrect, this represents a shift right and down) (C) y=|x|-6 (Incorrect, this represents a shift downward only) (D) y=|x+6| (Correct, this represents a shift to the left by 6 units)

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The graph of
y=|x| is shifted to the left by 6 units.
What is the equation of the new graph?
Choose 1 answer:
(A)
y=|x+6|-6
(B)
y=|x-6|-6
(C)
y=|x|-6
(D)
y=|x+6|

The graph of $y=|x|$ is shifted to the left by $6$ units. $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x+6|-6$ $\newline$ (B) $y=|x-6|-6$ $\newline$ (C) $y=|x|-6$ $\newline$ (D) $y=|x+6|$

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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 shifted to the left by

6

units.

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=|x+6|-6

\newline

(B)

y=|x-6|-6

\newline

(C)

y=|x|-6

\newline

(D)

y=|x+6|

Replace with $(x + 6)$ : To shift the graph of $y=|x|$ to the left by $6$ units, we need to replace $x$ with $(x + 6)$ in the equation. $\newline$ The transformation rule for horizontal shifts is: if a graph $y=f(x)$ is shifted to the left by $k$ units, the new graph will be $y=f(x+k)$ .
Apply transformation rule: Apply the transformation rule to the given function $y=|x|$ . The new equation after shifting to the left by $6$ units will be $y=|x+6|$ .
Check answer choices: Check the answer choices to see which one matches the transformed equation. $\newline$ (A) $y=|x+6|-6$ (Incorrect, this represents a shift left and down) $\newline$ (B) $y=|x-6|-6$ (Incorrect, this represents a shift right and down) $\newline$ (C) $y=|x|-6$ (Incorrect, this represents a shift downward only) $\newline$ (D) $y=|x+6|$ (Correct, this represents a shift to the left by $6$ units)