Unit 5: Piecewise Functions

Unit 5 Learning Targets

LT 5-1: I can graph an absolute value function.

LT 5-2: I can graph a piecewise function.

LT 5-3: I can graph a step function.

LT 5-4: I can use transformations to graph piecewise functions.

LT 5-1: The Absolute Value Function

The graph of an absolute value function has a vertex at the turning point, which represents either the minimum or maximum value of the function. The axis of symmetry is the vertical line that passes through the vertex.

Help Videos:

●      What Is an Absolute Value Function?

●      How Do You Graph an Absolute Value Function?

Practice:

5-1 Math XL

LT 5-2: Piecewise-Defined Functions

Piecewise-defined functions are functions whose domains are divided into intervals where each interval has a different function rule.

Help Videos:

●      What Is a Piecewise Linear Function?

●      How Do You Graph a Piecewise Function?

Practice:

5-2 Math XL

LT 5-3: Step Functions

A step function is a piecewise-defined function that pairs every number in an interval with a single value. Ceiling functions and floor functions are step functions that return the next integer greater or less than the input.

Help Videos:

●      How Do You Graph a Real-World Example of a Step Function?

●      What Is a Step Function?

Practice:

5-3 Math XL

LT 5-4: Transformations of Piecewise-Defined Functions

For the absolute value function, g(x)=a|x−h|+k, the values of the constants, h and k, translate the graph horizontally and vertically, and the value of the leading coefficient  a affects the vertical stretch or compression.

Help Videos:

●      How Do You Write an Equation for a Translation of an Absolute Value Function?

●      What Does the Constant a Do in y=a|x|?

Practice:

5-4 Math XL

Unit 5 Vocabulary

●      absolute value function

●      axis of symmetry

●      vertex

●      piecewise-defined function 

●      ceiling function

●      floor function

●      step function