Find g(x), where g(x) is the translation 2 units left of f(x) = |x|. Write your answer in the form a|x – h| + k, where a, h, and k are integers. g(x) = ______

Understanding the transformation: Understand the transformation required for f(x). A translation of 2 units left means that every x value in the function f(x) will be replaced by (x + 2) to shift the graph to the left.Applying the transformation: Apply the transformation to f(x). Since f(x) = |x|, the transformation 2 units left will give us g(x) = |x + 2|.Rewriting g(x) in the required form: Rewrite g(x) in the required form. The function g(x) = |x + 2| is already in the form a|x – h| + k, where a = 1, h = -2, and k = 0.

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Find $g(x)$ , where $g(x)$ is the translation $2$ units left 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, reflections, and dilations

Full solution

Q. Find

g(x)

, where

g(x)

is the translation

2

units left 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

Understanding the transformation: Understand the transformation required for $f(x)$ . $\newline$ A translation of $2$ units left means that every $x$ value in the function $f(x)$ will be replaced by $(x + 2)$ to shift the graph to the left.
Applying the transformation: Apply the transformation to $f(x)$ . $\newline$ Since $f(x) = |x|$ , the transformation $2$ units left will give us $g(x) = |x + 2|$ .
Rewriting g(x) in the required form: Rewrite $g(x)$ in the required form. $\newline$ The function $g(x) = |x + 2|$ is already in the form $a|x – h| + k$ , where $a = 1$ , $h = -2$ , and $k = 0$ .