Evaluating Functions: Domain and Range in Real Life

1. A car rental company charges a flat fee of $50 plus $0.20 per mile driven. Write a function to represent the total cost, C, as a function of miles driven, m. What is the domain of this function?

• m < 0

• m >= 0

• m = 50

• m <= 100

2. Using the function from question 1, evaluate the total cost for driving 100 miles. What is the range of this function based on the context?

• Total cost for driving 100 miles is C(100) = 100m + b. The range is [0, ∞) depending on m and b.

• The range is [-∞, 0] based on the context.

• Total cost for driving 100 miles is C(100) = 100m - b.

• Total cost for driving 100 miles is C(100) = 50m + b.

3. A local gym charges a monthly membership fee of $30 and an additional $5 for each class attended. Write a function to represent the total cost, C, as a function of the number of classes, c. What is the domain of this function?

• c < 0, c is a negative integer

• c >= 0, c is a non-negative integer

• c is any real number

• c <= 10, c is a positive integer

4. For the function in question 3, if a member attends 8 classes in a month, what is the total cost? Determine the range of this function based on the number of classes attended.

• Total cost for 8 classes is the same as attending 5 classes.

• Total cost for 8 classes is calculated by adding a flat fee.

• Total cost for 8 classes is 8 times the cost per class.

• Total cost for 8 classes is 4 times the cost per class.

5. A bakery sells cupcakes for $3 each and offers a discount for bulk orders. Write a function, C(x), to represent the cost of x cupcakes, where x is the number of cupcakes purchased. What is the domain of this function?

• x >= 0, where x is an integer

• x must be a prime number

• x is any negative integer

• x < 0, where x is a real number

6. If a customer buys 12 cupcakes, what is the total cost using the function from question 5? What is the range of this function?

• Total cost for 12 cupcakes is the cost per cupcake; range is from 0 to 12.

• Total cost for 12 cupcakes is 24 times the cost per cupcake; range is from 0 to 24.

• Total cost for 12 cupcakes is 12 times the cost per cupcake; range is from 0 to maximum total cost.

• Total cost for 12 cupcakes is 12 plus the cost per cupcake; range is from 0 to 12.

7. A smartphone plan costs $40 per month plus $0.10 per text message sent. Write a function to represent the total monthly cost, C, as a function of the number of text messages, t. What is the domain of this function?

• The domain is {t | t >= 0, t ∈ ℕ}

• The domain is {t | t > 0, t ∈ ℕ}

• The domain is {t | t >= 0, t ∈ ℤ}

• The domain is {t | t < 0, t ∈ ℕ}

9. A school is organizing a field trip and charges $15 per student. Write a function to represent the total cost, C, as a function of the number of students, s. What is the domain of this function?

• s >= 0, s is an integer

• s = 10, s is a positive integer

• s < 0, s is a real number

• s > 100, s is a whole number

10. If 25 students sign up for the field trip, what is the total cost? Determine the range of this function based on the number of students.

• The total cost is fixed regardless of the number of students.

• Total cost for 25 students is 25 times the cost per student.

• Total cost is calculated by adding the cost of each student individually.

• Total cost for 25 students is 50 times the cost per student.