WorksheetsReal-World Scenarios for Linear Functions
Total questions: 20
Worksheet time: 20mins
The following table shows what a local gym charges for nonmembers and members:
Find the cost for a member who uses the gym 12 times.
(a)
A dog groomer charges according to the following function f(x), which represents the total price and x represents the weight of the dog. If your dog weighs 40 pounds, how much will you pay?
$20
$30
$45
$0
A plumber charges a $25 service fee and $50 per hour for at least one hour but not more than 4 hours. If 𝑥 represents the number of hours the plumber is at your house, the total cost for the plumber’s service is represented by 𝑓(𝑥) = 50𝑥 + 25.
What is a possible range for this situation?
{1,2,3,4}
{75,125,175,225}
{𝑥 | 1 ≤ 𝑥 ≤ 4}
{𝑦 | 25 ≤ 𝑦 < 225}
A plumber charges a $25 service fee and $50 per hour for at least one hour but not more than 4 hours. If 𝑥 represents the number of hours the plumber is at your house, the total cost for the plumber’s service is represented by 𝑓(𝑥) = 50𝑥 + 25.
What is a possible domain for this situation?
{1,2,3,4}
{75,125,175,225}
{𝑥 | 1 ≤ 𝑥 ≤ 4}
{𝑦 | 25 < 𝑦 < 225}
Printer ink costs $16.89 per cartridge. The company that sells the ink cartridges charges a flat rate shipping fee of $4.25, no matter the number of cartridges purchased in a single order. Which linear function models the total cost, t, for a single order of c cartridges?
c = 21.14t
c = 16.89t + 4.25
t = 21.14c
t = 16.89c +4.25
Printer ink costs $18.99 per cartridge. The company that sells the ink cartridges charges a flat rate shipping fee of $7.95, no matter the number of cartridges purchased in a single order. Which linear function models the total cost, t, for a single order of c cartridges?
c = 26.94t
c = 18.99t + 7.95
t = 26.94c
t = 18.99c + 7.95
A new discount cell phone service charges $55 a month plus $15.00 for every line on the plan. Choose the linear function that represents the relationship between the number of lines (x) and the cost of the plan (y).
y = 70x
x = 70y
y = 55 + 15x
x = 55 + 15y
An online candy store sells 3 pounds of fudge for $54.99. Which function represents the relationship between x, the number of pounds of fudge ordered, and y, the total cost in dollars?
y=3(54.99)x
y=354.99x
y=(54.99−3)x
y=54.99x−3
Printer ink costs $16.89 per cartridge. The company that sells the ink cartridges charges a flat rate shipping fee of $4.25, no matter the number of cartridges purchased in a single order.
Which linear function models the total cost, t, for a single order of c cartridges?
c = 21.14t
c = 16.89t + 4.25
t = 21.14c
t = 16.89c +4.25
Ted's Taxi service charges a $5 pick up fee plus $2 per mile. Which function describes the situation?
y=5x+2
y=2x-5
y=5x-2
y=2x+5
A taxi company charges a flat fee of $3 plus $2 per mile driven. Write the function that represents the total cost (C) as a function of the number of miles driven (m). Then, interpret the rate of change and the initial value.
C(m) = 2m + 3
C(m) = 3m + 2
C(m) = 4m + 1
C(m) = 5m + 2
Ted's Taxi service charges a $5 pick up fee plus $2 per mile. Which function describes the situation?
y=5x+2
y=2x-5
y=5x-2
y=2x+5
Ashley is saving $18 that she earned for babysitting. She earns $7 every week for doing chores at home, which she also saves. Which function can be used to find t, the total amount of money Ashley will have saved at the end of w, weeks of doing chores?
t = 7w + 18
t = 18w + 7
t = 25w
t = 18w
The total cost, 𝑐, in dollars to create calendars for a fundraiser can be found using the function 𝑐 = 5.5𝑢 + 25 where u is the number of calendars made. If there are at least 10 calendars made, what is a possible domain for this function?
{𝑥 | 0 ≤ 𝑥 < 50}
{−12,−11,12,20,50}
{𝑥 | 10 ≤ 𝑥 < 100}
{10,11,12,13,14}
The total cost, 𝑐, in dollars to create calendars for a fundraiser can be found using the function 𝑐 = 5.5𝑢 + 25 where 𝑢 is the number of calendars made. If there are at least 10 calendars made, what is a possible range for this function?
{25,30.5,36,41.5,47}
{80,85.5,113,124,140.5}
{𝑦 | 0 ≤ 𝑦 < 25}
{𝑦 | 10 ≤ 𝑦 < 50}
The number of airplane trips, 𝑓(𝑝), needed to transport p people in one day can be found using the function f(p)=p/150 . If there are at most 750 people transported by airplanes daily, what is the domain of the function for this situation?
The set of all integers from 0 to 5
The set of all integers from 0 to 150
The set of all integers less than or equal to 750
The set of all integers from 0 to 750
A gym charges a $15 registration fee and $5 per session. If 𝑥 represents the number of sessions, the total cost for going to the gym is represented by 𝑓(𝑥) = 5𝑥 + 15. Mario will be going to the gym no more than 4 times this week. What is a possible domain for this situation?
{1,2,3,4}
{20,25,30,35}
{𝑥 | 0 ≤ 𝑥 ≤4}
{𝑦 | 15 ≤ 𝑦 ≤ 35}
A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 20x + 4.
What is the range of the function for this situation?
{0,1,2,3,4,5,6}
{4, 24, 44, 64, 84, 104, 124}
{0,2,4,6}
{4, 44, 84, 124}
A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If x pairs of plates are added to the barbell, the total weight of the barbell and plates in pounds can be represented by f(x) = 20x + 4.
What is the domain of the function for this situation?
{0,1,2,3,4,5,6}
{4, 24, 44, 64, 84, 104, 124}
{0,2,4,6}
{4, 44, 84, 124}
Joe had a summer job that pays $7.00 an hour and he worked between 15 and 25 hours every week. His weekly salary can be modeled by the equation: y = 7x, where y is his weekly salary and x is the number of hours he worked in a week. What is a reasonable domain for this function?
{15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25}
{105, 112, 119, 126, 133, 140, 147, 154, 161, 168}
{x | 15 ≤ x ≤ 25}
{x | 105 ≤ x ≤ 168}
