Unit 3 – Lesson 1 – Investigation 1: Homework
1) Lake Aid is an annual benefit show produced by the students of Wilde Lake High School to raise money for
the local food bank.
For each of the following functions:




Explain what the numbers in the function rule tell about the situation.
Explain what the function rule tells you to expect in the tables of values for the function.
Explain what the function rule tells you to expect in a graph of the function.
Write a NEXT/NOW rule for each.
a) Several of the show organizers researched the possibility of selling DVD’s of the show in order to increase
donations to the food bank. They would have to pay for recording of the show and for production of the
DVD’s. The cost (C) in dollars would depend on the number of DVD’s ordered (n) according to the rule:
𝑪 = 𝟏𝟓𝟎 + 𝟐𝒏.
b) Proceeds from ticket sales, after security and equipment rental fees are paid, are donated to the local food
bank. Once the ticket price was set, organizers determined that the proceeds (P) in dollars would depend on
the number of tickets sold (t) according to the rule: 𝑷 = 𝟔𝒕 − 𝟒𝟎𝟎.
c) The organizers of the event surveyed students to see how ticket price would affect the number of tickets
sold. The results of the survey showed that the number of tickets sold (T) could be predicted from the ticket
price (p) in dollars using the rule: 𝑻 = 𝟗𝟓𝟎 − 𝟕𝟓𝒑.
2) Match the following functions to their corresponding graphs without using a calculator.
a) 𝑦 = 𝑥
b) 𝑦 = 2𝑥 + 2
c) 𝑦 = 0.1𝑥 2
d) 𝑦 = 𝑥 + 2
e) 𝑦 = 9 − 0.5𝑥
3) The following graph shows the relationship between weekly profit and the number of customers per week
for Skate World Roller Rink.
a) Identify the slope and y – intercept of the line that best fits
this data.
b) What does the slope and y – intercept tell you about the
relationship between Skate World profit and the number of
customers per week?
c) If Skate World reached maximum capacity during each
skating session per week then admissions for that week
would equal 2400 customers. What would the rink’s profit be
in this situation?
4) The following table gives the amount of money spent on national health care for every 10 years from 1960
to 2000.
a) Was the amount of money spent on health care a
linear function over time from 1960 to 2000? How
can you tell without graphing the function?
b) What is the rate of change in health care expenditures from 1960 to 1970?
c) What is the rate of change in health care expenditures from 1970 to 1980?
d) What is the rate of change in health care expenditures from 1980 to 1990?
e) What is the rate of change in health care expenditures from 1990 to 2000?
f) What is the rate of change in health care expenditures from 1960 to 2000?
5) Linear functions can be used to describe the action of springs that stretch like those in telephone cords, and
springs that compress, like those in a mattress or a bathroom scale. Hooke’s Law in science says that, for an
ideal spring, the relationship between weight and length is perfectly linear, within the range of the spring. The
following table shows data from 4 different springs.
a) For each spring, identify the
length of the spring when there is no
weight applied
b) For each spring, identify the rate of change of the length of the spring as weight is increased. Specify units.
c) For each spring, identify whether the experiment was designed to measure spring stretch or spring
compression.
d) For each spring, write a NEXT / NOW equation to show how the spring length changes with each additional
ounce of weight.
e) Match the following rules with its corresponding spring.
1
𝑙 = 12 − 2 𝑤
1
𝑙 = 12 + 2 𝑤
𝑙 =5+𝑤
f) Match each spring to the correct graph in the following diagram.
Spring 1:
Spring 2:
Spring 3:
Spring 4:
𝑙 = 18 − 𝑤