Algebra 2 2-6 Complete Lesson: Families of Functions

By Matt Richardson

Last updated almost 3 years ago

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! The equation of the line is: 

How could you change the y-intercept so the graph of a second equation passes through point P?

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How could you change the slope so the graph of a second equation passes through point P?

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Problem 1 Got It? How are the functions related?

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Problem 1 Got It? How are the graphs of the functions related?

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Problem 1 Got It? Graph the functions on the same coordinate plane. Zoom and pan your graph to leave an appropriate scale and viewing window. After graphing, you may edit your responses to the previous 2 items.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

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Problem 2 Got It? Consider the projectile altitude f(x) of the airplane shown in Problem 2.

Suppose the flight leaves 30 minutes early. What function represents this transformation?

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Problem 3 Got It?

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Problem 4 Got It? For the function f(x) shown in Problem 4 and in the table below, what is the corresponding table for the transformation h(x)? Complete the table for h(x) on the canvas. Use a color other than black.

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Problem 4 Got It? Reasoning: If several transformations are applied to a graph, will changing the order of transformations change the resulting graph? Explain.

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Problem 5 Got It?

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Problem 5 Got It?

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Compare and Contrast: Part A: The graph below shows f(x) = 0.5x - 1.

Graph g(x) by translating f(x) up 2 units and then stretching it vertically by the factor 2.

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Compare and Contrast: Part B: The graph below shows f(x) = 0.5x - 1.

Graph h(x) by stretching f(x) vertically by the factor 2 and then translating it up 2 units.

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Reasoning: Can you give an example of a function for which a horizontal translation gives the same resulting graph as a vertical translation? Explain.

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Analysis: Find a new function g(x) transformed from f(x) = -x - 2 such that g(x) is perpendicular to f(x).

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Review Lesson 2-5: A musician's manager keeps track of the ticket prices and the attendance at recent performances in the table below.

Step 1. Use the embedded Desmos graphing utility below or visit desmos.com to create a scatterplot and to calculate and graph the line of best fit for the given data.
Step 2. Take a screenshot of your scatterplot and line of best fit.
Step 3. Upload your screenshot to the canvas below.

If you need a reminder of how to complete Step 1, review this video from the Desmos team and/or see Problem 3 from the Lesson 2-5 slideshow.

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Review Lesson 1-6: Resequence the items below to indicate the correct procedure for solving the absolute value equation.

Separate the equation |x - 3| = 5 into two equations: x - 3 = 5 and x - 3 = -5.
Solve the two equations separately to find two possible solutions: x = 8 and x = -2.
Since both solutions satisfy the equation, they are both solutions of the equation.
Isolate the |x - 3| part of the expression by subtracting 2 from each side of the equation.
Check both possible solutions by substituting them into the original equation, |x - 3| + 2 = 7.

Review Lesson 1-6: Fill in the blank: When solving absolute value equations, a possible solution that does not check out when substituted into the equation is called a(n) ?.

Vocabulary Review: Identify the items that are NOT vertical.

the y-axis
the x-axis
the horizon
columns
rows

Not vertical

Use Your Vocabulary: Complete each statement with the correct form of the word translation.

translate
translation
translatable

NOUN: The graph shows a vertical __?__ of the function.
ADJECTIVE: The toddler's language was not __?__.
VERB: The Spanish teacher helped the town mayor __?__ the letter.

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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Algebra 2 2-6 Complete Lesson: Families of Functions

How could you change the y-intercept so the graph of a second equation passes through point P?

How could you change the slope so the graph of a second equation passes through point P?

Problem 1 Got It? How are the functions related?

Problem 1 Got It? How are the graphs of the functions related?

Problem 1 Got It? Graph the functions on the same coordinate plane. Zoom and pan your graph to leave an appropriate scale and viewing window. After graphing, you may edit your responses to the previous 2 items.

Problem 2 Got It? Consider the projectile altitude f(x) of the airplane shown in Problem 2. Suppose the flight leaves 30 minutes early. What function represents this transformation?

Problem 3 Got It?

Problem 4 Got It? For the function f(x) shown in Problem 4 and in the table below, what is the corresponding table for the transformation h(x)? Complete the table for h(x) on the canvas. Use a color other than black.

Problem 4 Got It? Reasoning: If several transformations are applied to a graph, will changing the order of transformations change the resulting graph? Explain.

Problem 5 Got It?

Problem 5 Got It?

Compare and Contrast: Part A: The graph below shows f(x) = 0.5x - 1.Graph g(x) by translating f(x) up 2 units and then stretching it vertically by the factor 2.

Compare and Contrast: Part B: The graph below shows f(x) = 0.5x - 1.Graph h(x) by stretching f(x) vertically by the factor 2 and then translating it up 2 units.

Reasoning: Can you give an example of a function for which a horizontal translation gives the same resulting graph as a vertical translation? Explain.

Analysis: Find a new function g(x) transformed from f(x) = -x - 2 such that g(x) is perpendicular to f(x).

Review Lesson 1-6: Resequence the items below to indicate the correct procedure for solving the absolute value equation.

Review Lesson 1-6: Fill in the blank: When solving absolute value equations, a possible solution that does not check out when substituted into the equation is called a(n) __?__.

Vocabulary Review: Identify the items that are NOT vertical.

Use Your Vocabulary: Complete each statement with the correct form of the word translation.

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

Problem 2 Got It? Consider the projectile altitude f(x) of the airplane shown in Problem 2.

Suppose the flight leaves 30 minutes early. What function represents this transformation?

Compare and Contrast: Part A: The graph below shows f(x) = 0.5x - 1.

Graph g(x) by translating f(x) up 2 units and then stretching it vertically by the factor 2.

Compare and Contrast: Part B: The graph below shows f(x) = 0.5x - 1.

Graph h(x) by stretching f(x) vertically by the factor 2 and then translating it up 2 units.

Review Lesson 1-6: Fill in the blank: When solving absolute value equations, a possible solution that does not check out when substituted into the equation is called a(n) ?.

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.