Function: Word Problems

Function Word Problems

by Angela Weisheyer

Word Problem 1

​Goldie Blocks

Multiple Choice

Bob has a lot of gold bars that he has to carry. The weight of 1 gold bar is 27.4 pounds.

What is the independent variable?

• How strong Bob is.

• The total weight of all the gold.

• The number of gold bars Bob has.

• How many gold bars you are going to give your math teacher.

Multiple Choice

Bob has a lot of gold bars that he has to carry. The weight of 1 gold bar is 27.4 pounds.

What is the Dependent variable?

• How strong Bob is.

• The total weight of all the gold.

• The number of gold bars Bob has.

• How many gold bars you are going to give your math teacher.

Multiple Choice

Bob has a lot of gold bars that he has to carry. The weight of 1 gold bar is 27.4 pounds. Let x represent the number of gold bars.

Which function will represents the total weight?

• g(x) = 27.4x

• g(x) = 27.4 + x

• g(x) = x - 27.4

• g(x) = 27.4x + 1

Multiple Choice

Bob has a lot of gold bars that he has to carry. The weight of 1 gold bar is 27.4 pounds. Let x represent the number of gold bars.

What represents the limits of the domain?

• All Real Numbers

• All Whole Numbers

• All Integers

• All Natural Numbers

Multiple Choice

Bob has a lot of gold bars that he has to carry. The weight of 1 gold bar is 27.4 pounds. Let x represent the number of gold bars.

If Bob has no more than 2 gold bars which inequality represents the range?

• $$x\le2$$  

• $$0\le x\le2$$  

• $$g\le54.8$$  

• $$0\le g\le54.8$$  

Word Problem 2​

​Costly Hotel Vacation

Open Ended

A resort hotel charges 12.5% in taxes. Additionally, they charge a $25 resort fee. (The resort fee is not subject to sales tax.)

What are some important details in this problem that is needed to find the total cost of the hotel stay?

Multiple Choice

A resort hotel charges 12.5% in taxes. Additionally, they charge a $25 resort fee. (The resort fee is not subject to sales tax.)

The following functions represent the situation:

​

f(a)=1.125a

g(b)=b+25

What does the variable "a" represent?

• The cost of the hotel room and sales tax, but without the resort fee.

• The cost of the hotel room and resort fee, but without the sales tax.

• The cost of the hotel room without sales tax and without the resort fee.

• The total cost of the hotel stay.

Multiple Choice

A resort hotel charges 12.5% in taxes. Additionally, they charge a $25 resort fee. (The resort fee is not subject to sales tax.)

The following functions represent the situation:

​

What does the variable "b" represent?

• The cost of the hotel room and sales tax, but without the resort fee.

• The cost of the hotel room and resort fee, but without the sales tax.

• The cost of the hotel room without sales tax and without the resort fee.

• The total cost of the hotel stay.

Multiple Choice

A resort hotel charges 12.5% in taxes. Additionally, they charge a $25 resort. (The resort fee is not subject to sales tax.)

The following functions represent the situation:

What does f(a) represent?

• The cost of the hotel room and sales tax, but without the resort fee.

• The cost of the hotel room and resort fee, but without the sales tax.

• The cost of the hotel room without sales tax and without the resort fee.

• The total cost of the hotel stay.

Multiple Choice

A resort hotel charges 12.5% in taxes. Additionally, they charge a $25 resort. (The resort fee is not subject to sales tax.)

The following functions represent the situation:

What does g(b) represent?

• The cost of the hotel room and sales tax, but without the resort fee.

• The cost of the hotel room and resort fee, but without the sales tax.

• The cost of the hotel room without sales tax and without the resort fee.

• The total cost of the hotel stay.

Multiple Choice

Find g(f(a))

• g(f(a)) = 1.125(b+25)

• g(f(a)) = (1.125a) +25

• g(f(a)) = 1.125b+25

• g(f(a)) = (1.125a)(b+25

Open Ended

A resort hotel charges 12.5% in taxes. Additionally, they charge a $25. (The resort fee is not subject to sales tax.)

The following functions represent the situation:

f(a)=1.125a

g(b)=b+25

​What does the following represent

g(f(a)) = (1.125a) +25

Multiple Choice

​ A resort hotel charges 12.5% in taxes. Additionally, they charge a $25. (The resort fee is not subject to sales tax.)

The following functions represent the situation:

The cost of the hotel room without sales tax or the resort fee is $300. What is the total cost of the hotel stay.

• 362.5

• $362.50

• 365.625

• $365.63

Word Problem 3

The Price of Love​

Multiple Choice

The student government association is selling roses for Valentine’s Day to raise money for their trip to the state convention. The cost of each rose is $1.50 and the florist charges a delivery fee of $25. The class plans to sell the roses for $5.00 each.

What is the independent variables?

• The Profit

• The Total Cost

• The Number of Roses

• The Number of students

Multiple Choice

The student government association is selling roses for Valentine’s Day to raise money for their trip to the state convention. The cost of each rose is $1.50 and the florist charges a delivery fee of $25. The class plans to sell the roses for $5.00 each.

Write a cost function.

• C(x) = 1.5x + 25

• C(x) = 5x + 1.5

• C(x) = 1.5x - 25

• C(x) = 5x - 25

Open Ended

What does revenue mean?

Multiple Choice

The student government association is selling roses for Valentine’s Day to raise money for their trip to the state convention. The cost of each rose is $1.50 and the florist charges a delivery fee of $25. The class plans to sell the roses for $5.00 each.

Write a revenue function.

• R(x) = 5x 

• R(x) = 5x +25

• R(x) = 1.5x

• R(x) = 1.5x + 25

Open Ended

The student government association is selling roses for Valentine’s Day to raise money for their trip to the state convention. The cost of each rose is $1.50 and the florist charges a delivery fee of $25. The class plans to sell the roses for $5.00 each.

​

Cost    ​C(x) = 1.5x + 25               

Revenue    ​R(x) = 5x 

Now that we know the cost and the Revenue what else can we figure out?

Multiple Choice

The student government association is selling roses for Valentine’s Day to raise money for their trip to the state convention. The cost of each rose is $1.50 and the florist charges a delivery fee of $25. The class plans to sell the roses for $5.00 each.

Write a profit function.

• P(x) = C(x) - R(x)

• P(x) = R(x) - C(x)

• P(x) = C(x) + R(x)

• P(x) = R(C(x))

Multiple Choice

The student government association is selling roses for Valentine’s Day to raise money for their trip to the state convention. The cost of each rose is $1.50 and the florist charges a delivery fee of $25. The class plans to sell the roses for $5.00 each.

Simplify the expression P(x) = R(x) - C(x)

• P(x) = 3.5x+25

• P(x) = 6.5x + 25

• P(x) = -3.5x + 25

• P(x) = 3.5x - 25

Multiple Choice

The student government association is selling roses for Valentine’s Day to raise money for their trip to the state convention. The cost of each rose is $1.50 and the florist charges a delivery fee of $25. The class plans to sell the roses for $5.00 each.

If the florist will provide no more than 120 roses which inequality represents the profit range?

• $$x\le120$$  

• $$0\le x\le120$$  

• $$p\le395$$  

• $$0\le p\le395$$