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9-12 Algebra 1 Unit 5 Lesson 16

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Unit 5, Lesson 16

Finding and Interpreting Inverse Functions

Algebra 1

Practice

Problem 1

Student Task Statement

Tickets to a family concert cost $10 for adults and $3 for children. The concert organizers collected a total of $900 from ticket sales.

In this situation, what is the meaning of each variable in the equation ?
If 42 adults were at the concert, how many children attended?
If 140 children were at the concert , how many adults attended?
Write an equation to represent as a function of . Explain what this function tells us about the situation.
Write an equation to represent as a function of . Explain what this function tell us about the situation.

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Problem 2

Student Task Statement

A school group has $600 to spend on T-shirts. The group is buying from a store that gives them a $5 discount off the regular price per shirt.

gives the maximum number of shirts, , that can be purchased at a regular price, .

gives the regular price, , of a shirt when shirts are bought with all the money from the group.

What is when is 20?
What is when is 40?
Is one function an inverse of the other? Explain how you know.

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Problem 3

Student Task Statement

Functions and are inverses, and . Is the point on the graph of , on the graph of , or neither?

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Problem 4

Student Task Statement

Here are two equations that relate two quantities, and :

Select all statements that are true about and .

could represent a function, but could not.

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Problem 5

ForLesson 10: Domain and Range (Part 1)

Student Task Statement

Elena plays the piano for 30 minutes each practice day. The total number of minutes that Elena practiced last week is a function of , the number of practice days.

Find the domain and range for this function.

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Problem 6

ForLesson 11: Domain and Range (Part 2)

Student Task Statement

The graph shows the attendance at a sports game as a function of time in minutes.

Describe how attendance changes over time.

Piecewise function on coordinate plane, no grid, origin O. Horizontal axis, time in minutes, from 0 to 70 by 10’s. Vertical axis, attendance, from 0 to 60, by 20’s. Line starts at origin, moves upwards and to the right until 10 comma 50, then a slight uptick until 15 comma 55. Horizontal segment until 45 comma 55, then decline until 50 comma 45. Horizontal until 55 comma 45, then decreasing until 70 comma 0
Describe the domain.
Describe the range.

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Problem 7

ForLesson 11: Domain and Range (Part 2)

Student Task Statement

Two children set up a lemonade stand in their front yard. They charge $1 for every cup. The amount of money the children earned throughout the day, dollars, is a function of the number of cups of lemonade they sold, , up to that time. By the end of the day, they sell a total of 15 cups of lemonade.

Is 20 part of the domain of this function? Explain your reasoning.
What does the range of this function represent?
Describe the set of values in the range of .
Is the graph of this function discrete or continuous? Explain your reasoning.

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Problem 8

ForLesson 6: Features of Graphs

Student Task Statement

Here is the graph of function , which represents Andre's distance from his bicycle as he walked in a park.

Estimate .
Estimate .
For what values of does ?
For what values of does ?
For what values of does ?

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Lesson 16 Resources

Student Materials Student Materials in Spanish

Each equation could represent a function.

could represent a function, but could not.

The two equations represent two functions that are inverses of one another.

If represents a function, then the inverse function can be defined by .