Page 735 - Algebra 1

L E S S O N Graphing Absolute-Value Functions 107
Warm Up
1. Vocabulary A is the simplest function of a particular type, or
(Inv 6)
family.
Simplify.
2. 3 · 2 + 2⎪-5⎥
(5)
4. 4⎪x - 2⎥ = 60 (74)
3. 5 · 8 - 4⎪-6⎥ (5)
5. -3⎪x + 4⎥ = 36 (74)
New Concepts
A function whose rule has one or more absolute-value expressions is called an absolute-value function. The absolute-value parent function is f(x) = ⎪x⎥.
Graphing the Absolute-Value Parent Function
Graph the absolute-value parent function f(x) = ⎪x⎥. SOLUTION
Use a table to graph the function.
Example
1
x
y
-2
2
-1
1
0
0
1
1
2
2
8
4
x
4
The absolute-value parent function forms the shape of a “V.” The equation of the axis of symmetry of the absolute-value parent function is x = 0. The point on the axis of symmetry of the absolute-value graph, or the “corner” of the graph, is the vertex of an absolute-value graph.
The absolute-value function has two slopes. If the graph opens upward, the slope of the graph on the left of the axis of symmetry is -1. The slope of the graph on the right side of the axis of symmetry is 1.
axis of symmetry: x = 0
slope = 1
Math Reasoning
Write Why is “axis of symmetry” an appropriate name?
720 Saxon Algebra 1
y
-8
-4
8
-4
4
-8
y
2
slope = -1
x
4
-4
-2
2
-2
vertex: (0, 0)
-4