# Which of These is the Absolute Value Parent Function

Which of These is the Absolute Value Parent Function.

## Absolute Value Functions

An absolute value function is a role that contains an algebraic expression within absolute value symbols. Recall that the accented value of a number is its distance from



on the number line.

The absolute value parent role, written as

$f$

(
10
)

=

|

x

|

, is defined as


f

(
10
)

=

{

x
if
x
>

if
10
=

x
if
ten
<

To graph an absolute value role, choose several values of

$x$

and find some ordered pairs.

 $x$ $y$ = | 10 | −2 2 −ane 1 0 0 one 1 2 2

Plot the points on a coordinate plane and connect them.

Observe that the graph is V-shaped.

(

$1$

) The vertex of the graph is


(

,

)

.

(

$two$

) The centrality of symmetry (

$x$
=

or

$y$

-axis) is the line that divides the graph into two congruent halves.

(

$3$

) The domain is the prepare of all real numbers.

(

$4$

) The range is the set of all real numbers greater than or equal to



. That is,

$y$

.

(

$five$

) The

$x$

-intercept and the

$y$

-intercept are both



.

### Vertical Shift

To interpret the accented value part

$f$

(
x
)

=

|

ten

|

vertically, you tin can utilize the function

$m$

(
x
)

=
f

(
10
)

+
k

.

When

$k$
>

, the graph of

$\mathrm{grand}$

(
ten
)

translated

$k$

units up.

When

$\mathrm{yard}$
<

, the graph of

$g$

(
x
)

translated

$\mathrm{one thousand}$

units down.

### Horizontal Shift

To interpret the absolute value function

$f$

(
x
)

=

|

10

|

horizontally, yous can employ the function

$\mathrm{yard}$

(
10
)

=
f

(

10

h

)

.

When

$h$
>

, the graph of

$f$

(
x
)

is translated

$h$

units to the right to get

$g$

(
x
)

.

When

$h$
<

, the graph of

$f$

(
ten
)

is translated

$h$

units to the left to get

$g$

(
10
)

.

## Stretch and Compression

The stretching or compressing of the absolute value function

Read:   Humans Deplete the Most Resources When
$y$
=

|

x

|

is defined by the part

$y$
=
a

|

x

|

where

$a$

is a constant. The graph opens up if

$a$
>

and opens down when

$a$
<

.

For accented value equations multiplied by a constant

$\left($
for case,
y
=
a

|

x

|

)

,if


<
a
<
ane

, then the graph is compressed, and if

$a$
>
1

, it is stretched. As well, if a is negative, and then the graph opens downward, instead of upwards as usual.

More mostly, the class of the equation for an absolute value office is

$y$
=
a

|

x

h

|

+
k

. Also:

• The vertex of the graph is

(

h
,
chiliad

)

.

• The domain of the graph is fix of all real numbers and the range is
$y$

k

when

$a$
>

.

• The domain of the graph is set of all real numbers and the range is
$y$

k

when

$a$
<

.

• The axis of symmetry is
$x$
=
h

.

• It opens up if
$a$
>

and opens down if

$a$
<

.

• The graph
$y$
=

|

x

|

can be translated

$h$

units horizontally and

$\mathrm{thou}$

units vertically to get the graph of

$y$
=
a

|

x

h

|

+
k

.

• The graph
$y$
=
a

|

ten

|

is wider than the graph of

$y$
=

|

x

|

if


|

a

|

<
1

and narrower if


|
a
|

>
ane

.

## Which of These is the Absolute Value Parent Function

Source: https://www.varsitytutors.com/hotmath/hotmath_help/topics/absolute-value-functions

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