Math 2: Unit 5B Day 3 How do we solve problems using piecewise functions, step functions, and greatest integer functions?

2 Today’s Brainteaser Can you figure out the word/phrase represented by the puzzle? Square Roots Polygon Gone

Piecewise Functions A piecewise function is a function represented by more than a single equation. The domain indicates when to use each equation.

Evaluate the function: To evaluate a piecewise function, look at the domain!

Evaluate the function:

Points of discontinuity X-values where there are gaps in the graph Ex: *because there is a gap in the graph at x = 1, this is a point of discontinuity.

Graphing Piecewise Functions xyxy Domain: Range: Intercepts: Points of discontinuity:

Graphing Piecewise Functions xy xy Domain: Range: Intercepts: Points of discontinuity:

Graphing Piecewise Functions xy xy Domain: Range: Intercepts: Points of discontinuity:

Graphing Piecewise Functions xy xy Domain: Range: Intercepts: Points of discontinuity:

Writing an absolute value function as a piecewise function Graph the absolute value function Find linear equations that represent each piece of the graph Create a domain restriction based on the vertex Write the function as a piecewise function

Writing an absolute value function as a piecewise function Vertex: Open up or down? Left side of vertex: Right side of vertex:

Writing an absolute value function as a piecewise function Vertex: Open up or down? Left side of vertex: Right side of vertex:

Writing an absolute value function as a piecewise function Vertex: Open up or down? Left side of vertex: Right side of vertex: GA Notetaking Guide Page 52 – 53 # 1 – 7 all, #12 – 14 all

Step Function A piecewise function that is defined by a constant value over each part of its domain. Its graph resembles a set of stairs

Graph the following step functions

Greatest integer function: y = [x] The greatest integer function, y = [x] is defined as follows: [x] is the greatest integer that is less than or equal to x.

Reflection of the greatest integer function

Graph using transformations y=[x+3]y = [x-1]

Graph using transformations y=[x]+2 y = [x-2]+1

Real world applications of step functions In 2005 the cost C (in dollars) to send US postal service express mail up to 3 pounds depended on the weight w (in ounces) according to the function below. What is the cost to send a package weighing:  13 ounces?  3 ounces?  20 ounces?  5 ounces? REMEMBER: Test is ___________!!!! Do the REVIEW!!! HW: Page 52 (# 5 – 11) and Page 53 (# 5 – 10, 23 – 26)