Analyzing Real-World Scenarios with Piecewise Functions

A taxi company charges a flat fee of $5 for the first mile and $2 for each additional mile. Write a piecewise function to represent the cost of a taxi ride based on the number of miles traveled.

• C(m) = { 2m, m > 0 };

• C(m) = { 5 + 3(m - 1), m > 1 }

• C(m) = { 5 + 2m, m >= 0 }

• C(m) = { 5, 0 < m <= 1; 5 + 2(m - 1), m > 1 }

A gym charges a monthly fee of $30 for up to 10 classes. For each class beyond 10, there is an additional charge of $5 per class. Create a piecewise function to represent the total cost based on the number of classes attended.

• C(n) = { 30, if n < 10; 30 + 5(n - 10), if n >= 10 }

• C(n) = { 30, if n <= 10; 30 + 5(n - 10), if n > 10 }

• C(n) = { 20, if n <= 10; 20 + 5(n - 10), if n > 10 }

• C(n) = { 30 + 5n, if n <= 10; 30 + 5(n - 5), if n > 10 }

A delivery service charges $10 for the first 5 pounds and $1.50 for each additional pound. Write a piecewise function to express the cost of delivery based on the weight of the package.

• C(w) = { 10, 0 < w <= 3; 10 + 2 * (w - 3), w > 3 }

• C(w) = { 10, 0 < w <= 5; 10 + 1.5 * (w - 5), w > 5 }

• C(w) = { 10, 0 < w <= 10; 10 + 1 * (w - 10), w > 10 }

• C(w) = { 5, 0 < w <= 5; 5 + 2 * (w - 5), w > 5 }

A concert ticket costs $50 for the first 100 tickets sold. After that, the price increases to $75. Create a piecewise function to represent the ticket price based on the number of tickets sold.

• P(n) = { 50, if n <= 100; 75, if n > 100 }

• P(n) = { 50, if n < 100; 100, if n >= 100 }

• P(n) = { 50, if n <= 50; 75, if n > 50 }

• P(n) = { 50, if n < 100; 75, if n >= 100 }

A phone plan costs $20 for the first 500 MB of data and $0.10 for each additional MB. Write a piecewise function to represent the monthly cost based on the amount of data used.

• C(x) = { 20, x <= 500; 20 + 0.15 * (x - 500), x > 500 }

• C(x) = { 20, 0 <= x < 500; 20 + 0.05 * (x - 500), x >= 500 }

• C(x) = { 20, x < 500; 20 + 0.20 * (x - 500), x >= 500 }

• C(x) = { 20, 0 <= x <= 500; 20 + 0.10 * (x - 500), x > 500 }

A parking garage charges $10 for the first hour and $2 for each additional hour. Create a piecewise function to represent the total parking fee based on the number of hours parked.

• f(h) = { 10, h = 2; 10 + 2(h - 2), h > 2 }

• f(h) = { 5, h = 1; 5 + 2(h - 1), h > 1 }

• f(h) = { 10, h = 0; 10 + 3(h - 1), h > 0 }

• f(h) = { 10, h = 1; 10 + 2(h - 1), h > 1 }

A water park charges $25 for the first 3 hours and $5 for each additional hour. Write a piecewise function to express the total cost based on the number of hours spent at the park.

• C(h) = { 20, 0 < h <= 3; 20 + 5(h - 3), h > 3 }

• C(h) = { 30, 0 < h <= 3; 30 + 5(h - 3), h > 3 }

• C(h) = { 25, 0 < h <= 3; 25 + 5(h - 3), h > 3 }

• C(h) = { 25, 0 < h <= 2; 25 + 5(h - 2), h > 2 }

A library fines $0.50 for each day a book is overdue for the first 5 days, and $1 for each day after that. Create a piecewise function to represent the total fine based on the number of days overdue.

• F(d) = { 0.50 * d, if 0 <= d <= 5; 2.50 + 1 * (d - 5), if d > 5 }

• F(d) = { 0.50 * d, if d < 5; 1.50 + 1 * (d - 5), if d >= 5 }

• F(d) = { 0.50 * d, if d <= 3; 1 * (d - 3), if d > 3 }

• F(d) = 0.50 * d, if d < 5; 1 * (d - 5), if d >= 5

A subscription service charges $15 for the first month and $10 for each subsequent month. Write a piecewise function to represent the total cost based on the number of months subscribed.

• C(m) = { 10, if m = 1; 10(m), if m > 1 }

• C(m) = { 15, if m = 1; 20(m - 1), if m > 1 }

• C(m) = { 15, if m = 1; 15 + 10(m - 1), if m > 1 }

• C(m) = { 15, if m = 1; 15 + 5(m - 1), if m > 1 }

A school charges $100 for the first 10 students and $80 for each additional student. Create a piecewise function to represent the total cost based on the number of students enrolled.

• C(n) = { 100 + 80n, if n <= 10; 100 + 80(n - 10), if n > 10 }

• C(n) = { 100 + 80(n - 10), if n <= 10; 100, if n > 10 }

• C(n) = { 100, if n <= 10; 100 + 80(n - 10), if n > 10 }

• C(n) = { 80, if n <= 10; 100 + 80(n - 10), if n > 10 }