The graph of y=|x| is scaled vertically by a factor of 6 . What is the equation of the new graph? Choose 1 answer: (A) y=|x-6| (B) y=6|x| (C) y=(1)/(6)|x| (D) y=|x-(1)/(6)|

Multiply by 6: Vertical scaling of a graph by a factor means multiplying the output (y-value) by that factor. The original equation is y = |x|. To scale it vertically by a factor of 6, we multiply the entire right side of the equation by 6. Calculation: y = 6 * |x|Check given options: Now we need to check the given options to see which one matches our calculation. (A) y = |x - 6| is a horizontal translation, not a vertical scaling. (B) y = 6|x| is exactly what we calculated. (C) y = (1/6)|x| is a vertical compression, not a scaling by a factor of 6. (D) y = |x - (1/6)| is a horizontal translation, not a vertical scaling.

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The graph of
y=|x| is scaled vertically by a factor of 6 .
What is the equation of the new graph?
Choose 1 answer:
(A)
y=|x-6|
(B)
y=6|x|
(C)
y=(1)/(6)|x|
(D)
y=|x-(1)/(6)|

The graph of $y=|x|$ is scaled vertically by a factor of $6$ . $\newline$ What is the equation of the new graph? $\newline$ Choose $1$ answer: $\newline$ (A) $y=|x-6|$ $\newline$ (B) $y=6|x|$ $\newline$ (C) $y=\frac{1}{6}|x|$ $\newline$ (D) $y=\left|x-\frac{1}{6}\right|$

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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

6

\newline

What is the equation of the new graph?

\newline

Choose

1

answer:

\newline

(A)

y=|x-6|

\newline

(B)

y=6|x|

\newline

(C)

y=\frac{1}{6}|x|

\newline

(D)

y=\left|x-\frac{1}{6}\right|

Multiply by $6$ : Vertical scaling of a graph by a factor means multiplying the output ( extit{y}-value) by that factor. The original equation is $y = |x|$ . To scale it vertically by a factor of $6$ , we multiply the entire right side of the equation by $6$ . $\newline$ Calculation: $y = 6 \cdot |x|$
Check given options: Now we need to check the given options to see which one matches our calculation. $\newline$ (A) $y = |x - 6|$ is a horizontal translation, not a vertical scaling. $\newline$ (B) $y = 6|x|$ is exactly what we calculated. $\newline$ (C) $y = (\frac{1}{6})|x|$ is a vertical compression, not a scaling by a factor of $6$ . $\newline$ (D) $y = |x - (\frac{1}{6})|$ is a horizontal translation, not a vertical scaling.