Find g(x), where g(x) is the reflection across the y-axis of f(x) = |x|. Write your answer in the form a|x – h| + k, where a, h, and k are integers. g(x) = ______

Replace x with -x: To find the reflection of the function f(x) = |x| across the y-axis, we need to replace every x in the function with -x. This is because reflecting a function across the y-axis changes the sign of the x-coordinates.Apply transformation to g(x): The original function is f(x) = |x|. To reflect this function across the y-axis, we apply the transformation x to -x, which gives us g(x) = |(-x)|.Simplify g(x): Since the absolute value function has the property that |a| = |-a| for any real number a, we can simplify g(x) = |(-x)| to g(x) = |x|.Express g(x) in a|x-h|+k form: Now we need to express g(x) in the form a|x – h| + k, where a, h, and k are integers. Since g(x) = |x| is already in this form with a = 1, h = 0, and k = 0, we can write g(x) = 1|x - 0| + 0.

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Find $g(x)$ , where $g(x)$ is the reflection across the $y$ -axis of $f(x) = |x|$ . $\newline$ Write your answer in the form $a|x - h| + k$ , where $a$ , $h$ , and $k$ are integers. $\newline$ $g(x) =$ ______ $\newline$

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Math Problems

Algebra 1

Transformations of absolute value functions: translations and reflections

Full solution

Q. Find

g(x)

, where

g(x)

is the reflection across the

y

-axis of

f(x) = |x|

\newline

Write your answer in the form

a|x - h| + k

, where

a

h

, and

k

are integers.

\newline

g(x) =

______

\newline

Replace $x$ with $-x$ : To find the reflection of the function $f(x) = |x|$ across the y-axis, we need to replace every $x$ in the function with $-x$ . This is because reflecting a function across the y-axis changes the sign of the $x$ -coordinates.
Apply transformation to $g(x)$ : The original function is $f(x) = |x|$ . To reflect this function across the y-axis, we apply the transformation $x$ to $-x$ , which gives us $g(x) = |(-x)|$ .
Simplify $g(x)$ : Since the absolute value function has the property that $|a| = |-a|$ for any real number $a$ , we can simplify $g(x) = |(-x)|$ to $g(x) = |x|$ .
Express $g(x)$ in $a|x-h|+k$ form: Now we need to express $g(x)$ in the form $a|x – h| + k$ , where $a$ , $h$ , and $k$ are integers. Since $g(x) = |x|$ is already in this form with $a = 1$ , $h = 0$ , and $a|x-h|+k$ $0$ , we can write $a|x-h|+k$ $1$ .