The graph of y=|x| is shifted down by 6 units and to the left by 9 units. What is the equation of the new graph? Choose 1 answer: (A) y=|x+9|-6 (B) y=|x-9|+6 (C) y=|x+9|+6 (D) y=|x-9|-6

Understanding Shifts: To determine the equation of the transformed graph, we need to understand how shifts affect the equation of a function. A shift to the left by 9 units will add 9 to the x-value inside the absolute value. A shift down by 6 units will subtract 6 from the entire function.Applying Horizontal Shift: Applying the horizontal shift to the left by 9 units to the function y = |x|, we replace x with (x + 9) to get y = |x + 9|.Applying Vertical Shift: Next, we apply the vertical shift down by 6 units to the function y = |x + 9|. We subtract 6 from the entire function to get y = |x + 9| - 6.Comparing Transformed Equation: Now we compare the transformed equation y = |x + 9| - 6 with the given choices to find the correct answer.

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The graph of
y=|x| is shifted down by 6 units and to the left by 9 units.
What is the equation of the new graph?
Choose 1 answer:
(A)
y=|x+9|-6
(B)
y=|x-9|+6
(C)
y=|x+9|+6
(D)
y=|x-9|-6

The graph of $y=|x|$ is shifted down by $6$ units and to the left by $9$ units. $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x+9|-6$ $\newline$ (B) $y=|x-9|+6$ $\newline$ (C) $y=|x+9|+6$ $\newline$ (D) $y=|x-9|-6$

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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 down by

6

units and to the left by

9

units.

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=|x+9|-6

\newline

(B)

y=|x-9|+6

\newline

(C)

y=|x+9|+6

\newline

(D)

y=|x-9|-6

Understanding Shifts: To determine the equation of the transformed graph, we need to understand how shifts affect the equation of a function. A shift to the left by $9$ units will add $9$ to the $x$ -value inside the absolute value. A shift down by $6$ units will subtract $6$ from the entire function.
Applying Horizontal Shift: Applying the horizontal shift to the left by $9$ units to the function $y = |x|$ , we replace $x$ with $(x + 9)$ to get $y = |x + 9|$ .
Applying Vertical Shift: Next, we apply the vertical shift down by $6$ units to the function $y = |x + 9|$ . We subtract $6$ from the entire function to get $y = |x + 9| - 6$ .
Comparing Transformed Equation: Now we compare the transformed equation $y = |x + 9| - 6$ with the given choices to find the correct answer.