Functions and Transformations

Lesson 3

Math

Unit 5

9th Grade

Lesson 3 of 16

Objective


Evaluate a piecewise function written algebraically, with and without context.

Common Core Standards


Core Standards

  • F.IF.A.1 — Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
  • F.IF.A.2 — Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
  • A.SSE.A.1.A — Interpret parts of an expression, such as terms, factors, and coefficients.

Foundational Standards

  • 8.EE.B.5
  • 8.EE.B.6
  • 8.F.B.4

Criteria for Success


  1. Determine the appropriate equation to use when evaluating a piecewise function, given a specific domain. 
  2. Distinguish between the outputs and inputs of piecewise functions, and use appropriate equations to evaluate accordingly.
  3. Evaluate piecewise functions and interpret in context.
  4. Describe, in terms of the graph of the function and the subdomains in the piecewise function, why only particular inputs are applied to particular pieces of the function. 
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Anchor Problems


Problem 1

A piecewise graph is defined below.

          

Evaluate the values below.

  1.   $${f(-8)}$$
  2.   $${f(-4)}$$
  3.   $${f\left({3\over4}\right)}$$
  4.   $${f(3)}$$
  5.   $${f(3.01)}$$
  6.   $${f(5)}$$

Guiding Questions

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Problem 2

In order to gain popularity among students, a new pizza place near school plans to offer a special promotion. The cost of a large pizza (in dollars) at the pizza place as a function of time (measured in days since February 10th) may be described as

(Assume $$t$$ only takes whole number values.)

  1. If you want to give their pizza a try, on what date(s) should you buy a large pizza in order to get the best price?
  2. How much will a large pizza cost on February 18th?
  3. On what date, if any, will a large pizza cost $${$13}$$?
  4. Write an expression that describes the sentence "The cost of a large pizza is at least $$A$$ dollars $$B$$ days into the promotion" using function notation and mathematical symbols only.
  5. Calculate $${C(9)-C(8)}$$ and interpret its meaning in the context of the problem.
  6. On average, the cost of a large pizza goes up about $${85}$$ cents per day during the first two weeks of the promotion period. Which of the following equations best describes this statement?

Guiding Questions

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References

Illustrative Mathematics Pizza Place Promotion

Pizza Place Promotion, accessed on May 10, 2018, 10:46 a.m., is licensed by Illustrative Mathematics under either the CC BY 4.0 or CC BY-NC-SA 4.0. For further information, contact Illustrative Mathematics.

Problem Set


Give your students more opportunities to practice the skills in this lesson with a downloadable problem set aligned to the daily objective.

Target Task


A museum offers discounted rates for large groups following the rules below.

  1. How much would it cost for a group of 25 people to go to the museum?
  2. A school is planning on buying 29 tickets to the museum. A student says that it is more cost effective to buy 30 tickets than 29 tickets. Do you agree with the student? What is the difference in cost for 29 tickets vs. 30 tickets? 

Additional Practice


The following resources include problems and activities aligned to the objective of the lesson that can be used for additional practice or to create your own problem set.

  • Include examples of evaluating piecewise functions, with and without context; a simple search should generate several examples.
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Lesson 2

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Lesson 4

Lesson Map

A7CB09C2-D12F-4F55-80DB-37298FF0A765

Topic A: Piecewise Functions

Topic B: Absolute Value Functions

Topic C: Function Transformations

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