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Algebra 2 8-2 Complete Lesson: The Reciprocal Function Family

By Matt Richardson
Last updated about 3 years ago
26 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! For a class party, the students will share the cost for the hall rental. Each student will also have to pay $8 for food. The cost of the hall rental is already graphed. What effect does the food cost have on the graph?

Problem 1 Got It? Which statements below are true regarding the graph of the function?
Select all that apply.

Problem 1 Got It? Graph the three functions on the same plane. Zoom and pan your graph to establish an approprite viewing window. Consider the similarities and differences of the graphs. Think about domain, range, intercepts, asymptotes, etc. and how they relate to the the equation of each function.

Problem 2 Got It?

Problem 2 Got It?

Problem 2 Got It?

Problem 3 Got It? What is the graph of the function? Identify its domain and range. Include graph detail.
Use Desmos to check your work and make any necessary edits AFTER first graphing by hand.

Problem 4 Got It? The graph below is a translation of the graph of


What is an equation of the function?

Problem 5 Got It? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.

Respond to each question on the right with the appropriate response from the left.

  • All real numbers
  • Whole numbers from 1 to 312
  • Integers from -13 to 325
  • 173 students
  • 162 students
  • 160 students
  • If every student who attends shares the facility cost equally, what function models the cost per student C with respect to the number of students n who attend?
  • What is the domain of the function? Consider only the domain values that make sense in the context of the problem.
  • How many students must attend to make the cost per student no more than $7.50 per student?

Problem 5 Got It? The junior class is renting a laser tag facility with a capacity of 325 people. The cost for the facility is $1200. The party must have 13 adult chaperones.

Respond to each question on the right with the appropriate response from the left.

  • All real numbers
  • Whole numbers from 1 to 282
  • 190 students
  • 172 students
  • 165 students
  • Suppose the class wants to promote the event by giving away 30 free admissions to the event. What new function models the cost per student C with respect to the number of students n who attend?
  • What is the domain of the new function? Consider only the domain values that make sense in the context of the problem.
  • now, how many students must attend to make the cost per student no more than $7.50 per student?

Graphing:
1. Without the aid of a graphing utility, sketch a graph the equation on the canvas below using the blue ink tool.
2. Graph the equation on the embedded Desmos graphing calculator above.
3. Sketch a copy of the Demos graph on the canvas below using the red ink tool.
4. Consider any discrepancies between the graphs.
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

Vocabulary: What transformation changes the graph of the first equation into the graph of the second?

Open Ended: Write an equation of a stretch and a reflection of the graph of the equation across the x-axis.

Writing: Explain how you can tell if a function in the form shown is a stretch or compression of the parent function. Reference values of 'a' in your response.

Review Lesson 8-1: Suppose that x and y vary inversely . Match a modeling function from the left with each inverse variation on the right and find y when x = -5.

  • When x = -5, y = -10.
  • When x = -5, y = -4.8.
  • When x = -5, y = -9.6.
  • Inverse variation: x = 2 when y = 12.
  • Inverse variation: x = 25 when y = 2.
  • Inverse variation: x = 12 when y = 4.

Review Lesson 7.1: Without graphing, determine and indicate whether each function on the right represents exponential growth or exponential decay. Also, determine and indicate the y-intercept of each function on the right.

  • y-intercept: 0.1
  • y-intercept: 5
  • y-intercept: 3
  • Exponential growth
  • Exponential decay

Review Lesson 6-3: Identify the product of each expression on the left. Match each expression with its product on the right.

Review Lesson 4-4: Factor the quadratic expression.

Review Lesson 4-4: Factor the quadratic expression.

Vocabulary Review: Identify the reciprocal(s) from the list.

Vocabulary Review: Classify each statement as eitherTrue or False.

  • The reciprocal of a positive number is positive.
  • The reciprocal of a negative number is positive.
  • A negative number has no reciprocal.
  • The reciprocal of 0 is undefined.
  • True
  • False

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