Algebra 2/Trig
Name: ____________________________________
Section 2.6 Notes - Special Functions p. 124
Piecewise Function: A function defined by at least two equations, each of which applies to a different part of the
function’s ___________________.
Example 1: Evaluate the following function when (a) 𝑥 = 1 and (b) 𝑥 = 5
2𝑥 − 1, 𝑖𝑓 𝑥 ≤ 1
𝑔(𝑥) = {
3𝑥 + 1, 𝑖𝑓 𝑥 > 1
Checkpoint 1: Evaluate the following function for the given input.
9𝑥 − 4, 𝑖𝑓 𝑥 > 3
𝑓(𝑥) = {1
𝑥 + 1, 𝑖𝑓 𝑥 ≤ 3
2
a) 𝑓(−4)
b) 𝑓(5)
1
Example 2: Graph the function 𝑓(𝑥) = {
− 2 𝑥 − 1, 𝑖𝑓 𝑥 < 2
3𝑥 − 2, 𝑖𝑓 𝑥 ≥ 2
c) 𝑓(3)
3
− 2 𝑥 − 1, 𝑖𝑓 𝑥 < −2
Example 3: Graph the function 𝑓(𝑥) = { 𝑥 + 1, 𝑖𝑓 − 2 ≤ 𝑥 ≤ 1
𝑖𝑓 𝑥 > 1
3,
STEP FUNCTIONS
The Greatest Integer Function
In Calc: MATH. NUM. int( or round(
Example 4:
Greatest-Integer Function
Or Rounding Down Function
OR Rounding Up Function
Rounding Up Function
x
y
0
0
x
y
0.3
0
-1.7
-1
0.9
0
-1
-1
1
1
0
0
1.1
1
2.5
3
2.3
2
2.5
2
3.7
4
2.7
2
4.1
5
Example 5: What happens to the graph of 𝑓(𝑥) = [𝑥] when we have (𝑥) = 2[𝑥] ?
Graph both and look at the table.
ABSOLUTE VALUE FUNCTION: f(x) =
Parent Function for Absolute Value Functions:
The graph of 𝑦 = |𝑥| is __________________ and is __________________ about the ____________. For every
point (x, y) on the graph, the point (-x, y) is also on the graph.
Vertex: The __________________________ point on the absolute value graph. The vertex of the graph 𝑦 = |𝑥| is
________.
Example 6: Graph 𝑓(𝑥) = 2|𝑥| − 1. Then graph its inverse.
x
-2
-1
0
1
2
y