Lesson 4-­‐1 Piecewise Functions Recall the parent function for absolute value: How could we rewrite the absolute value parent function as two different functions? 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.
Describe the graph as completely as possible. Is the graph a function?
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. Example #3: Graph. −2, 𝑤ℎ𝑒𝑛 𝑥 < 0 𝑦 = 1,
𝑤ℎ𝑒𝑛 0 ≤ 𝑥 ≤ 2 5, 𝑤ℎ𝑒𝑛 𝑥 > 2
Lesson 4-­‐1 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. You try: Graph the function.