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Algebra 1 4-6 Complete Lesson: Formalizing Relations and Functions

By Matt Richardson
Last updated almost 3 years ago
31 Questions
Note from the author:
A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

Solve It! Your friend is playing a board game. He is on the space shown in the diagram. He rolled a 3 to get to that space. On which spaces could he have started before rolling the 3? Select all that apply.

Problem 1 Got It? Identify the domain and range of the relation.
Place each value only once.

  • 4.2
  • 1.5
  • 5
  • 2.2
  • 7
  • 4.8
  • 0
  • Domain
  • Range

Problem 1 Got It? Represent the relation with a mapping diagram.

Problem 1 Got It? Is the relation a function?

Problem 1 Got It? Identify the domain and range of the relation.
Place each value only once.

  • -1
  • 1
  • -2
  • 2
  • 4
  • -4
  • 7
  • -7
  • Domain
  • Range

Problem 1 Got It? Represent the relation with a mapping diagram.

Problem 1 Got It? Is the relation a function?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? Use the function in Problem 3, w(x) = 250x. How many words can you read in 6 min? Enter only a number.

Problem 4 Got It?

Problem 5 Got It?

Problem 5 Got It?

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Identify the domain of the relation.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Identify the range of the relation.

Consider the relation {(-2, -3), (-1, 4), (0, 5), (1, 6)}.

Represent the relation with a mapping diagram. Remember to label the domain and range in your diagram.

Is the relation in the graph a function? Use the vertical line test.

What is f(2) for the function f(x) = 4x + 1?

The domain of f(x), defined below, is {-4, -2, 0, 2, 4}. What is the range?

Vocabulary: Write y = 2x + 7 using function notation.

Compare and Contrast: You can use a mapping diagram or the vertical line test to tell if a relation is a function. Which method do you prefer? Explain.

Error Analysis: A student drew the dashed line on the graph shown and concluded that the graph represented a function. Is the student correct? Explain.

Review Lesson 4-5: Match each function rule with the situation it models.

  • E = 7 + 5h
  • a = 4.5s + 10
  • You buy several pairs of socks for $4.50 per pair, plus a shirt for $10. The total amount a you spend is a function of the number of pairs of socks you buy.
  • You babysit for $5 per hour and get a $7 tip. Your earnings E are a function of the number of hours h you work.

Review Lesson 4-1: The graph shows a family's distance from home as they drive to the mountains for a vacation. Label the variables in the graph.

  • variable
  • Number of trips
  • Time
  • Elevation
  • Number of deer spotted
  • Distance from home

Review Lesson 4-1: Describe how the variables are related at the indicated points on the graph.

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4.

  • x = 1
  • x = 2
  • x = 3
  • x = 4
  • Expression = 18
  • Expression = 12
  • Expression = 9
  • Expression = 15

Review Lesson 1-2: Evaluate the expression for x = 1, 2, 3, and 4. Only use each x-value once.
Not all expression value categories will be used.

  • x = 1
  • x = 2
  • x = 3
  • x = 4
  • Expression = 7
  • Expression = 15
  • Expression = 29
  • Expression = 22
  • Expression = 8

Vocabulary Review: Use the words in the left column to label the function machine in the image below. Use each word once.

  • function rule
  • y-values
  • output
  • x-values
  • input
  • range
  • Region A
  • Region B
  • Region C

Use Your Vocabulary: Complete each sentence with the appropriate word from the column on the left. Use each word once.

  • reasonable
  • reasonableness
  • unreasonable
  • The student estimated to check the __?__ of her answer.
  • Sales tax of $32 on an $85 item is __?__.
  • A price of $14 is __?__ for a pizza.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.

For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success