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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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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 $k = 0$ .

More problems from Transformations of absolute value functions: translations, reflections, and dilations

Question

g(x)

g(x)

is the reflection across the

y

f(x) = |x|

\newline

Write your answer in the form

a|x - h| + k

a

h

k

\newline

g(x) =

\newline

Posted 2 months ago

Question

y=|x|

is reflected across the

x

-axis and then scaled vertically by a factor of

7

\newline

What is the equation of the new graph?

\newline

1

\newline

y=7|x|

\newline

y=-7|x|

\newline

y=\frac{1}{7}|x|

\newline

y=-\frac{1}{7}|x|

Posted 2 months ago

Question

y=|x|

is scaled vertically by a factor of

6

\newline

What is the equation of the new graph?

\newline

1

\newline

y=|x-6|

\newline

y=6|x|

\newline

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

\newline

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

Posted 1 month ago

Question

y=|x|

is scaled vertically by a factor of

\frac{1}{3}

\newline

What is the equation of the new graph?

\newline

1

\newline

y=|x|-3

\newline

y=-3|x|

\newline

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

\newline

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

Posted 2 months ago

Question

y=|x|

is shifted to the left by

6

\newline

What is the equation of the new graph?

\newline

1

\newline

y=|x+6|-6

\newline

y=|x-6|-6

\newline

y=|x|-6

\newline

y=|x+6|

Posted 1 month ago

Question

y=|x|

is reflected across the

x

-axis and then scaled vertically by a factor of

\frac{1}{4}

\newline

What is the equation of the new graph?

\newline

1

\newline

y=-4|x|

\newline

y=|x|-4

\newline

y=-\frac{1}{4}|x|

\newline

y=|x-4|

Posted 2 months ago

Question

y=|x|

is shifted down by

9

\newline

What is the equation of the new graph?

\newline

1

\newline

y=|x|-9

\newline

y=|x+9|

\newline

y=|x|+9

\newline

y=|x-9|

Posted 4 months ago

Question

\begin{array}{l} y=\frac{1}{3} x+5 \\ y=2 x \end{array}

\newline

Consider the given system of equations. If

(x, y)

is the solution to the system, then what is the value of

y+x

Posted 1 month ago

Question

\frac{1}{3} x+3 y=4

\newline

2 x-4=2 y

\newline

Consider the given system of equations. If

(x, y)

is the solution to the system, then what is the value of

x-y

Posted 1 month ago

Question

Isabel tried to evaluate an expression step by step.

(2+8)+8

. Find Isabel's first mistake

Posted 13 hours ago