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
$\mathrm{}$on the number line.
The absolute value parent role, written as
$f$, is defined as
$$
To graph an absolute value role, choose several values of
$x$and find some ordered pairs.
$x$ 
$y$ 
−2  2 
−ane  1 
0  0 
one  1 
2  2 
Plot the points on a coordinate plane and connect them.
Observe that the graph is Vshaped.
(
$1$) The vertex of the graph is
$$.
(
$\mathrm{two}$) 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
$\mathrm{}$. That is,
$y$.
(
$\mathrm{five}$) The
$x$intercept and the
$y$intercept are both
$\mathrm{}$.
Vertical Shift
To interpret the accented value part
$f$vertically, you tin can utilize the function
$m$
.
When
$k$, the graph of
$\mathrm{grand}$translated
$k$units up.
When
$\mathrm{yard}$, the graph of
$g$translated
$\mathrm{one\; thousand}$units down.
Horizontal Shift
To interpret the absolute value function
$f$horizontally, yous can employ the function
$\mathrm{yard}$
.
When
$h$, the graph of
$f$is translated
$h$units to the right to get
$g$.
When
$h$, the graph of
$f$is translated
$h$units to the left to get
$g$.
Stretch and Compression
The stretching or compressing of the absolute value function
$y$is defined by the part
$y$where
$a$is a constant. The graph opens up if
$a$and opens down when
$a$.
For accented value equations multiplied by a constant
$($,if
$\mathrm{}$, then the graph is compressed, and if
$a$, 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
$y$. 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/absolutevaluefunctions