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Algebra 1 4-5 Complete Lesson: Writing a Function Rule

By Matt Richardson
Last updated almost 3 years ago
29 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! You and a friend are swimming 20 laps at the local pool. One lap is across the pool and back. You both swim at the same rate. Your friend started first. The trail of arrows shows how far he has already swum. What equation gives the distance you have swum as a function of the distance your friend has swum? Let y = your distance and x = your friend's distance.

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Solve It! How far have you swum when your friend finishes his 20 laps?

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Problem 1 Got It?

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Problem 2 Got It?

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Problem 2 Got It?

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Problem 3 Got It? Write a function rule for the area A of a triangle whose height h is 4 in. more than twice the length of its base b. Hint: You should only use two variable, A and b.

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Problem 3 Got It? What is the area of the triangle from the previous item when the length of its base is 16 in.?

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Problem 3 Got It? Reasoning: Graph the function rule from Problem 3 that is provided provided below. How do you know the rule is nonlinear?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

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Vocabulary: Suppose you write an equation that gives a as a function of b. Which is the dependent variable?

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Error Analysis: A worker has dug 3 holes for fence posts. It will take 15 min to dig each additional hole. Your friend writes the rule t = 15n + 3 for the time t, in minutes, required to dig n additional holes. Describe and correct your friend's error.

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Reasoning: Is the graph of a function rule that relates a square's area to its side length continuous or discrete?

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Review Lesson 4-4: Graph the function rules on the same plane.

Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

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Review Lesson 2-6: Match equivalent amounts.

  • 8.25 lb
  • 450 cm
  • 17 yd
  • 90 s
  • 216 h
  • 9.5 km
  • 1.5 min
  • 132 oz
  • 9,500 m
  • 51 ft
  • 9 days
  • 4.5 m

Review Lesson 1-6: Find the product. Simplify if necessary.
Enter only a number.

Review Lesson 1-6: Find the product. Simplify if necessary.
Enter only a number.

Review Lesson 1-6: Find the product. Simplify if necessary.
Enter only a number.

Review Lesson 1-6: Find the product. Simplify if necessary.
Enter only a number.

Review Lesson 1-6: Find the product. Simplify if necessary.
Enter only an improper fraction.

Vocabulary Review: In function notation, you read f(x) as "f of x." You can think of the value "f(x)" as another way of writing "y." Write how you would read h(g) aloud.

Vocabulary Review: Label the equations based on whether or not they are written using function notation.

  • function notation
  • not function notation
  • f(x) = 2x + 1
  • xy = f
  • f(x) = 1 - x
  • y = 8f

Use Your Vocabulary: Consider the rule. For b, c, and d ≠ 0,
Which equation is an example of this rule?

Use Your Vocabulary: Fill in the blank: The reason that rule in the previous item states that b, c, and d ≠ is because __?__.

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

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