Week 12-8.1 Absolute Value Function

An absolute value function is a function that contains an algebraic expression within absolute value symbols. Recall that the absolute value of a number is its distance from ‘O(zero) on the number line.

The absolute value parent function, written as $f (x) = | x |$ , is defined as: Absolute Value function (Piecewise)

To graph an absolute value function, choose several values of $x$ and find some ordered pairs.

$x$	$y = \| x \|$
−2	2
−1	1
0	0
1	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 $(0, 0)$ .

( $2$ ) The axis of symmetry ( $x = 0$ or $y$ -axis) is the line that divides the graph into two congruent halves.

( $3$ ) The domain is the set of all real numbers.

( $4$ ) The range is the set of all real numbers greater than or equal to $0$ . That is, $y \geq 0$ .

( $5$ ) The $x$ -intercept and the $y$ -intercept are both O.

Practice: Graph

$x$	$y = \| x \|$
-4	2
-3	1
-2	0
-1	1
0	0

Plot the points on a coordinate plane and connect them.

y = | x + 2 |

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