1. 2.5 Using Piecewise Functions (Part 2)

2. Vocabulary Piecewise Function Points of Discontinuity Step Function
At Least two equations, each of which applies to a different part of the function’s domain
Points of Discontinuity
Points on the graph of a function in which there is a break, hole, or gap
Step Function
Piecewise function that is continuous
Looks like stairs

3. Vocabulary Extrema: Average rate of change:
Maximum or Minimum of function
Local
(within given domain)
Global
(within entire domain)
Average rate of change:
Slope of a line through two points

4. To Write a Piecewise Function
Graph the function if not already graphed
Break it into parts
Changes in slope or direction
Identify the domain for each part
Write an equation for each domain

5. Write a piecewise function for f(x) = 2│x + 4 │- 6
Vertex = (- 4,- 6)

6. What is the Extrema and rate of change of f(x) = 2│x + 4 │- 6?
Since the vertex is (- 4,- 6), the minimum (extrema) is - 6.
When x > - 4, the rate of change (slope) is 2.
When x < - 4, the rate of change (slope) is - 2.

7. Do #8 on p. 50 with a partner.

8. Step Functions
Write a piecewise function for the step function shown. Describe any intervals over which the function is constant.

9. Do #7 on p. 50 with a partner.

10. Homework
Notetaking Guide
Pg. 52, 1 – 14 all