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Algebra 2 6-6 Complete Lesson: Function Operations

Last updated almost 4 years ago
25 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.
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Solve It! You want to buy a sofa that was marked down by $100 before the clearance discount was applied.

The furniture store may add the 5% sales tax before applying the additional discount, or it may add the sales tax after applying the additional discount. Which way is better for you, the customer?

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Solve It! In the above item, how much do you save by choosing the less expensive option?
Enter your response in this format: $12.30

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Problem 1 Got It?

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Problem 2 Got It?

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Problem 3 Got It?

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Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 15% discount and then the 20% discount.

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Problem 4 Got It? A store is offering a 15% discount on all items. Also, employees get a 20% discount (20% off original price(s)). Write a composite function to model taking the 20% discount and then the 15% discount.

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Problem 4 Got It? Reasoning: In the scenario above, which order of discounts results in a lower cost to the employee?

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50

Error Analysis: Your friend used some simple functions and found the following to be true for particular functions f and g and concluded that function composition is commutative.

Give an example to show that your friend is mistaken.
Define each of the following in your counterargument:
f(x)
g(x)
(f °g)(x)
(g ° f)(x)
Note: To form a counterexample, (f °g)(x) should not equal (g ° f)(x).

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Open-Ended: Find two functions f and g such that, for all real numbers x

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Review Lesson 6-5: Identify the solution(s) to each equation on the right. Be sure to check for extraneous solutions.

  • -2
  • 0
  • 1
  • 2
  • 3
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Review Lesson 5-7: Expand the binomial. Respond with a polynomial in standard form.
Recall the Binomial Theorem and Pascal's triangle.
Do not use commas in coeffients.

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Review Lesson 3-1: Graph the system. Take note of the solution(s). Zoom and pan your graph to establish and appropriate viewing window.

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Review Lesson 3-1: Graph the system. Take note of the solution(s). Zoom and pan your graph to establish and appropriate viewing window.

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Vocabulary Review: Identify the item(s) from the left that match the categories on the right. (Each category will contain a single item from the left.)

  • input
  • output
  • Represents function notation and can be read "g of x"
  • Shows a function rule
  • The function rule below represents the cost of a number of tons f wheat t.
    The number of tons of wheat is the __?__ of the function.
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Use Your Vocabulary: Complete each sentence with the correct form of the word composite.

  • composite
  • composition
  • compose
  • VERB: The musician worked to __?__ a new piece of music.
  • ADJECTIVE: A __?__ number has more than two factors.
  • NOUN: The poster was a __?__ of photos and famous quotes.
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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.

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Reflection: Math Success