GRAPHING ABSOLUTE VALUE FUNCTIONS

Finding Vertex of Absolute Value Functions

To find the vertex of absolute value function, we have to compare the given function with vertex form

y = a|x - h| + k

Here (h, k) is vertex.

For example,

y = 2|x + 1| - 3

To find vertex of the function above, we compare with vertex form.

y = 2|x - (-1)| - 3

Vertex is at (-1, -3).

x and y intercepts

To find x - intercept, we will apply y = 0. For example,

y = 2|x + 1| - 3

x-intercept :

Put y = 0

0 = 2|x + 1| - 3

2|x + 1| = 3

|x + 1| = 3/2

x-intercepts are (1/2, 0) and (-5/2, 0)

y-intercept :

Put x = 0

y = 2|0 + 1| - 3

y = 2 - 3

y = -1

y-intercept is at (0, -1).

Slope and Reflections
(or) Direction of Opening

The function which is in the form

y = a|x - h| + k

a is slope and the sign of a will decide the reflections.

• If a is positive, the curve will open up.
• If a is negative, the curve will open down.

For example,

y = 2|x + 1| - 3

Slope = 2, since the sign of a is positive, the curve will open up. 

Domain and Range

All possible inputs is known as domain.

For those inputs, the set of values what we are receiving is range.

For example,

y = 2|x + 1| - 3

All real values is domain. Range is (3, ∞).

Increasing and Decreasing Interval

If the curve opens up,

• to the left of minimum, it is decreasing
• to the right of minimum, it is increasing.

If the curve open down,

• to the left of maximum, it is increasing.
• to the right of maximum, it is decreasing.