The graph of y=|x| is scaled vertically by a factor of (1)/(3). What is the equation of the new graph? Choose 1 answer: (A) y=|x|-3 (B) y=-3|x| (C) y=(1)/(3)|x| (D) y=|x|-(1)/(3)

Calculate New Equation: Vertical scaling of a graph by a factor of k means multiplying the output (y-value) by k. In this case, the factor is (1)/(3), so we multiply the y-value of the original function y=|x| by (1)/(3). Calculation: New equation y = (1)/(3) * |x|Check Answer Choices: Check the answer choices to see which one matches the new equation y = (1)/(3) * |x|. (A) y=|x|-3 (This is a vertical shift, not a scaling.) (B) y=-3|x| (This is a vertical scaling by -3, not (1)/(3).) (C) y=(1)/(3)|x| (This matches our calculation.) (D) y=|x|-(1)/(3) (This is a vertical shift, not a scaling.)

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The graph of
y=|x| is scaled vertically by a factor of
(1)/(3).
What is the equation of the new graph?
Choose 1 answer:
(A)
y=|x|-3
(B)
y=-3|x|
(C)
y=(1)/(3)|x|
(D)
y=|x|-(1)/(3)

The graph of $y=|x|$ is scaled vertically by a factor of $\frac{1}{3}$ . $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x|-3$ $\newline$ (B) $y=-3|x|$ $\newline$ (C) $y=\frac{1}{3}|x|$ $\newline$ (D) $y=|x|-\frac{1}{3}$

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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 scaled vertically by a factor of

\frac{1}{3}

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=|x|-3

\newline

(B)

y=-3|x|

\newline

(C)

y=\frac{1}{3}|x|

\newline

(D)

y=|x|-\frac{1}{3}

Calculate New Equation: Vertical scaling of a graph by a factor of $k$ means multiplying the output (y-value) by $k$ . In this case, the factor is $\frac{1}{3}$ , so we multiply the y-value of the original function $y=|x|$ by $\frac{1}{3}$ . $\newline$ Calculation: New equation $y = \frac{1}{3} \cdot |x|$
Check Answer Choices: Check the answer choices to see which one matches the new equation $y = \frac{1}{3} \cdot |x|$ .
(A) $y=|x|-3$ (This is a vertical shift, not a scaling.)
(B) $y=-3|x|$ (This is a vertical scaling by $-3$ , not $\frac{1}{3}$ .)
(C) $y=\frac{1}{3}|x|$ (This matches our calculation.)
(D) $y=|x|-\frac{1}{3}$ (This is a vertical shift, not a scaling.)