Sign up for FREE

Algebra 2 6-7 Complete Lesson: Inverse Relations and Functions

Last updated about 4 years ago

29 questions

Note from the author:

10

F.BF.1.c

10

F.BF.4.a

10

F.BF.4.c

F.IF.1

10

F.BF.4.a

F.BF.4.c

F.IF.7.a

10

F.BF.4.a

10

F.BF.4.a

F.IF.1

10

F.IF.1

10

F.BF.4.a

10

F.BF.1.b

F.BF.1.c

10

N.RN.2

10

F.IF.7.a

10

F.IF.1

10

100

10

F.BF.4.a

F.BF.4.c

F.IF.1

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.

Question 1

1.

Solve It! What's wrong with the headline? Why? What is a more appropriate headline?

Question 2

2.

Problem 1 Got It? What are the graphs of t and its inverse? Represent both relations as mapping diagrams on the canvas.

Question 3

3.

10

Question 4

4.

Problem 2 Got It?

A

F.BF.4.a

Question 5

5.

Problem 3 Got It? Graph the function, its inverse, and the line y = x on the same plane.
Note that the function and its inverse should be reflective across the line y = x.
Zoom and pan your graph to establish an appropriate viewing window.

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

10

Question 6

6.

Problem 4 Got It?

F.BF.4.a

F.IF.1

10

Question 7

7.

Problem 4 Got It?

A

F.BF.4.a

10

Question 8

8.

Problem 4 Got It?

F.BF.4.a

F.IF.1

10

Question 9

9.

Problem 4 Got It?

F.BF.4.a

F.IF.1

10

Question 10

10.

A

B

F.BF.4.a

Question 11

11.

10

Question 12

12.

Problem 6 Got It?

A

F.BF.4.a

10

Question 13

13.

Problem 6 Got It?

F.BF.4.a

F.IF.1

10

Question 14

14.

What is the inverse of f ? Is the inverse a function?

F.BF.4.a

F.IF.1

10

Question 15

15.

What is the inverse of f ? Is the inverse a function?

F.BF.4.a

F.IF.1

10

Question 16

16.

A

F.BF.4.a

F.IF.1

10

Question 17

17.

A

B

F.BF.4.a

10

Question 18

18.

A

B

F.BF.4.a

10

Question 19

19.

A

B

F.BF.4.a

Question 21

21.

Reasoning: A function consists of the pairs (2, 3), (x, 4), and (5, 6). What values, if any, may x not assume?

Question 22

22.

Error Analysis: A classmate says the following.
Show that this is incorrect by finding examples of f(x) and g(x) for which the equation does not hold.

Question 23

23.

Review Lesson 6-6: For the given functions f, g, and h, match each function operation and composition on the left with the equivalent simplified expression on the right.

Question 24

24.

Review Lesson 6-1: Find each real root.

No real roots

Question 25

25.

Review Lesson 4-1: Graph the functions on the same plane.
Note how the functions are transformations of the parent quadratic function y = x2.
Zoom and pan your graph to establish an appropriate viewing window.

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

Question 26

26.

Vocabulary Review: Fill in each blank on the right with the appropriate item from the left.

Consider the relation below for some items.

y-
x-

Question 27

27.

Use Your Vocabulary: Categorize the domains and ranges on the left.

Use the relation r, as defined here.

Domain of r
Range of r

Question 28

28.

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.

Question 29

29.

Reflection: Math Success

If you decrease an amount x by 20%, you have 0.8x. If you then increase 0.8x by 20%, you get (0.8x)(1.2) = 0.96x, which is less than the original amount x. The headline states that the mayor's salary was restored, but the mayor's salary will be 4% less than the original salary. A more appropriate headline would be Most of Mayor's Salary Restored.

If you decrease an amount x by 20%, you have 0.2x. If you then increase 0.2x by 20%, you get (0.2x)(1.2) = 0.24x, which is less than the original amount x. The headline states that the mayor's salary was restored, but the mayor's salary will be 76% less than the original salary. A more appropriate headline would be Some of Mayor's Salary Restored. 

Problem 1 Got It? Reasoning: Is t a function? Is the inverse of t a function? Explain.

t is a function; the inverse of t is not a function because there are two y-values for one x-value.

t is not a function; the inverse of t is also not a function; in both t and its inverse, there are two y-values for at least one x-value. 

t is a function; the inverse of t is also a function: in both t and its inverse, there is only one y-value for each x-value.  

t is a function; the inverse of t is also a function because there is only one y-value for each x-value. 

B

C

D

A

B

C

D

B

C

D

A

B

C

D

A

B

C

D

Problem 5 Got It? The function d, below, relates the distance d, in meters, that an object has fallen to its velocity, v, in meters per second. 
What is the inverse of this function?

If a cliff diver falls from a height of 24 meters, what is his velocity in meters per second as he enters the water? 

C

D

Problem 6 Got It? Given g(x) below, find g-1(x). 

B

C

D

A

B

C

D

A

B

C

D

A

B

C

D

What is the inverse of f ? Is the inverse a function? 
 

B

C

D

C

D

C

D

For h, find the value for x for which the equality 
(h ◦ h-1)(x) = x does not hold. 

C

D

For the relation to be a function, x may not assume 2, 3, 4, 5, or 6.

For the relation to be a function, x may not assume 2 or 5.

For the relation to be a function, x may not assume 3, 4, or 5.

x may assume any real number and the relation will still represent a function.

The domain of a relation is the set of inputs, also called the __?__ coordinates of the ordered pair.

The range of a relation is the set of inputs, also called the __?__ coordinates of the ordered pair. 

The domain of the relation above is __?__.

The range of the relation above is __?__.

Domain of the inverse of r

Range of the inverse of r