Lesson 4-‐1
Piecewise Functions
Recall the parent function for absolute value:
The graphs of both y = x − 2 for x < 3 and y = −2x + 7 for x ≥ 3 are shown on the same coordinate grid below.
How could we rewrite the absolute value parent function as two different functions?
Lesson 4-‐1
A piecewise function is a function that is defined using different rules for the different nonoverlapping intervals of its domain.
To evaluate any piecewise function for a specific x-‐value: 1. Find the interval of the domain that contains that input 2. Use the rule for that interval.
Example #1: Evaluate the Piecewise function for x = -‐1 and x = 4.
You try:: Evaluate the Piecewise Function for x = -‐2 and x =0.
Lesson 4-‐1
Example #2: Graph the function. Then identify the domain and range.
Example #3: Graph the function. Then identify the domain and range.
𝑦 = 4𝑥, 𝑤ℎ𝑒𝑛 𝑥 > 1−𝑥 + 3, 𝑤ℎ𝑒𝑛 𝑥 ≤ 1
Lesson 4-‐1
You try: Graph the function. Then identify the domain and range.
𝑦 = −𝑥, 𝑤ℎ𝑒𝑛 𝑥 > 32𝑥 + 1, 𝑤ℎ𝑒𝑛 𝑥 ≤ 3
Example #4: Graph the function. Then identify the domain and range.
𝑦 =−2, 𝑤ℎ𝑒𝑛 𝑥 < 0 1, 𝑤ℎ𝑒𝑛 0 ≤ 𝑥 ≤ 2 5, 𝑤ℎ𝑒𝑛 𝑥 > 2
A hole is an open circle on the graph.A piecewise function that is constant for each interval of its domain is called a step function.
Lesson 4-‐1
You try: Graph the function. Then identify the domain and range.
Example #5: Write the piece-‐wise function whose graph is shown.
State the domain and range of the graph.
