Find g(x), where g(x) is the translation 1 unit down of f(x) = |x|. Write your answer in the form a|x – h| + k, where a, h, and k are integers. g(x) = ______

Understanding downward translation: Understand the effect of translating a function downward. Translating a function downward by k units involves subtracting k from the function's value. The general form of the translation is g(x) = f(x) - k.Applying the translation to the given function: Apply the translation to the given function. Since we want to translate f(x) = |x| one unit down, we set k = 1 and apply the translation to f(x). g(x) = f(x) - 1 g(x) = |x| - 1Writing the translated function in required form: Write the translated function in the required form. The question asks us to write the answer in the form a|x - h| + k. Since there is no horizontal translation or reflection, h = 0 and a = 1. The vertical translation is one unit down, so k = -1. g(x) = 1|x - 0| - 1

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Find $g(x)$ , where $g(x)$ is the translation $1$ unit down 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 2

Transformations of absolute value functions

Full solution

Q. Find

g(x)

, where

g(x)

is the translation

1

unit down 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 downward translation: Understand the effect of translating a function downward. $\newline$ Translating a function downward by $k$ units involves subtracting $k$ from the function's value. The general form of the translation is $g(x) = f(x) - k$ .
Applying the translation to the given function: Apply the translation to the given function. $\newline$ Since we want to translate $f(x) = |x|$ one unit down, we set $k = 1$ and apply the translation to $f(x)$ . $\newline$ $g(x) = f(x) - 1$ $\newline$ $g(x) = |x| - 1$
Writing the translated function in required form: Write the translated function in the required form. $\newline$ The question asks us to write the answer in the form $a|x - h| + k$ . Since there is no horizontal translation or reflection, $h = 0$ and $a = 1$ . The vertical translation is one unit down, so $k = -1$ . $\newline$ $g(x) = 1|x - 0| - 1$