NAME _____________________________________________ DATE ____________________________ PERIOD _____________
2-6 Study Guide and Intervention
Special Functions
Piecewise-Defined Functions A piecewise-defined function is written using two or more expressions. Its graph is
often disjointed.
Example: Graph f(x) = { 𝟐𝒙 𝐢𝐟 𝒙 < 𝟐
𝒙 − 𝟏 𝐢𝐟 𝒙 ≥ 𝟐.
First, graph the linear function f(x) = 2x for x < 2. Since 2 does not satisfy this
inequality, stop with a circle at (2, 4). Next, graph the linear function
f(x) = x – 1 for x ≥ 2. Since 2 does satisfy this inequality, begin with a dot at (2, 1).
Exercises
Graph each function. Identify the domain and range.
𝑥 + 2 if 𝑥 < 0
1. f (x) = {2𝑥 + 5 if 0 ≤ 𝑥 ≤ 2
−𝑥 + 1 if 𝑥 > 2
−𝑥 − 4 if 𝑥 < −7
2. f (x) = {5𝑥 − 1 if − 7 ≤ 𝑥 ≤ 0
2𝑥 + 1 if 𝑥 > 0
𝑥
3
if 𝑥 ≤ 0
3. h(x) = {2𝑥 − 6 if 0 < 𝑥 < 2
1 if 𝑥 ≥ 2
Chapter 2
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Glencoe Algebra 2
NAME _____________________________________________ DATE ____________________________ PERIOD _____________
2-6 Study Guide and Intervention (continued)
Special Functions
Step Functions and Absolute Value Functions
Name
Written as
Greatest Integer Function
f(x) = ⟦𝑥⟧
Absolute Value Function
f (x) = ⎪x⎥
Graphed as
two rays that are mirror images of each other and meet at a point, the vertex
Example: Graph f(x) = 3 ⎪x⎥ – 4.
Find several ordered pairs. Graph the points and connect
them. You would expect the graph to look similar to its
parent function, f(x) = ⎪x⎥ .
x
3 ⎥x⎥ – 4
0
–4
1
–1
2
2
–1
–1
–2
2
Exercises
Graph each function. Identify the domain and range.
1. f(x) = 2⟦𝑥⟧
Chapter 2
3. f(x) = ⟦𝑥⟧ + 4
2. h(x) = ⎪2x + 1⎥
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Glencoe Algebra 2