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Math · Algebra 1 · Unit 5

Unit 5: Functions

Students expand and deepen their understanding of functions, working with function notation, features of graphs, domain and range, piecewise and absolute value functions, and inverse functions.

Worksheets

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Unit
📝 Worksheet ✅ Answer guide
Concept
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Practice
Set 1
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Set 2
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Advanced
Set 1
📝 Worksheet ✅ Answer key
Set 2
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What this unit covers

A Functions and Their Representations · 5 lessons
Goals
  • Sketch a graph of a function given statements in function notation.
  • Understand that a relationship between two quantities is a function if there is only one possible output for each input.
  • Write equations that represent rules using function notation.
Lessons
  1. Describing and Graphing Situations
  2. Function Notation
  3. Interpreting and Using Function Notation
  4. Using Function Notation to Describe Rules (Part 1)
  5. Using Function Notation to Describe Rules (Part 2)
B Analyzing and Creating Graphs of Functions · 4 lessons
Goals
  • Given a graph of a function, estimate or calculate the average rate of change over a specified interval.
  • Interpret key features of a graph—the intercepts, maximums, minimums, and intervals when the function is increasing or decreasing—in terms of a situation.
  • Interpret statements about two or more functions written in function notation.
Lessons
  1. Features of Graphs
  2. Using Graphs to Find Average Rate of Change
  3. Interpreting and Creating Graphs
  4. Comparing Graphs
C A Closer Look at Inputs and Outputs · 5 lessons
Goals
  • Interpret an absolute value function described in words or in function notation, and create a table of values and a graph to represent the function.
  • Interpret the graph of a piecewise function or its rules given in function notation, and explain the rules (orally and in writing) in terms of a situation.
  • Understand that the domain of a function is the set of all possible inputs and the range is the set of all possible outputs.
Lessons
  1. Domain and Range (Part 1)
  2. Domain and Range (Part 2)
  3. Piecewise Functions
  4. Absolute Value Functions (Part 1)
  5. Absolute Value Functions (Part 2)
D Inverse Functions · 3 lessons
Goals
  • Find the inverse of a linear function by solving an equation for the input variable.
  • Write a linear function and an inverse function to model data and solve problems.
Lessons
  1. Inverse Functions
  2. Finding and Interpreting Inverse Functions
  3. Writing Inverse Functions to Solve Problems
E Let's Put It to Work · 1 lesson
Lessons
  1. Using Functions to Model Battery Power
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Adapted from the Illustrative Mathematics curriculum (v.360), licensed CC BY-NC 4.0. © Illustrative Mathematics.