Mastering Piecewise Functions: Word Problems & Graphing

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. Graph the function for up to 5 miles.

• C(m) = { 5, 0 < m <= 1; 2m + 4, m > 1 }

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

• C(m) = { 5, 0 < m <= 1; 2m + 3, m > 1 }

• C(m) = { 5, m < 1; 3m + 2, 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. How would you graph this function?

• C(n) = { 30, 0 <= n <= 10; 30 + 5(n - 10), n > 10 }

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

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

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

A delivery service charges $10 for the first 5 pounds and $1.50 for each additional pound. Write a piecewise function to represent the cost of delivery based on the weight of the package. Graph the function for weights up to 15 pounds.

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

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

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

• C(w) = { 10, 0 < w <= 3; 10 + 1 * (w - 3), w > 3 }

A concert ticket costs $50 for the first 100 tickets sold. After that, the price increases to $75. Write a piecewise function to represent the ticket price based on the number of tickets sold. How would you graph this function?

• P(x) = { 50, for 0 <= x <= 50; 75, for x > 50 }

• P(x) = { 50, for 0 <= x <= 200; 75, for x > 200 }

• P(x) = { 50, for 0 <= x <= 100; 100, for x > 100 }

• P(x) = { 50, for 0 <= x <= 100; 75, for x > 100 }

A phone plan costs $20 for the first 2 GB of data and $10 for each additional GB. Write a piecewise function to represent the monthly cost based on data usage. Graph the function for data usage up to 10 GB.

• C(x) = { 20, 0 <= x <= 2; 20 + 10(x - 2), x > 2 }

• C(x) = { 30, 0 <= x <= 2; 30 + 10(x - 2), x > 2 }

• C(x) = { 10, 0 <= x <= 2; 10 + 5(x - 2), x > 2 }

• C(x) = { 20, 0 <= x <= 5; 20 + 15(x - 5), x > 5 }

A parking garage charges $5 for the first hour and $2 for each additional hour. Write a piecewise function to represent the parking fee based on the number of hours parked. How would you graph this function for up to 6 hours?

• f(x) = { 5, 0 < x <= 1; 2x + 3, x > 1 } for 0 < x <= 6

• f(x) = { 5, 0 < x <= 1; 3x - 1, x > 1 } for 0 < x <= 6

• f(x) = { 5, 0 < x <= 2; 2x, x > 2 } for 0 < x <= 6

• f(x) = { 5, x < 1; 2x + 5, x >= 1 } for 0 < x <= 6

A bakery sells cupcakes for $3 each for the first dozen and $2.50 each for any additional cupcakes. Create a piecewise function to represent the cost based on the number of cupcakes purchased. Graph the function for up to 24 cupcakes.

• C(x) = { 3x, 1 <= x <= 12; 36 + 3(x - 12), 13 <= x <= 24 }

• C(x) = { 3x, 1 <= x <= 24 }

• C(x) = { 3x, 1 <= x <= 12; 36 + 2.5(x - 12), 13 <= x <= 24 }

• C(x) = { 2.5x, 1 <= x <= 12; 30 + 3(x - 12), 13 <= x <= 24 }

A library fines $0.25 per day for the first 5 days a book is overdue and $1.00 per day after that. Write a piecewise function to represent the total fine based on the number of days overdue. How would you graph this function?

• F(d) = { 0.50d, 0 <= d <= 5; 1.00 + (d - 5), d > 5 }

• F(d) = { 0.25d, 0 <= d <= 10; 1.00 + (d - 10), d > 10 }

• F(d) = { 0.10d, 0 <= d <= 5; 0.50 + (d - 5), d > 5 }

• F(d) = { 0.25d, 0 <= d <= 5; 1.25 + (d - 5), d > 5 }

A water park charges $20 for the first 3 hours and $5 for each additional hour. Write a piecewise function to represent the cost of admission based on the number of hours spent at the park. Graph the function for up to 8 hours.

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

• C(h) = { 20, 0 < h <= 4; 20 + 10(h - 4), h > 4 }

• C(h) = { 15, 0 < h <= 3; 15 + 5(h - 3), h > 3 }

• C(h) = { 20, 0 < h <= 2; 20 + 5(h - 2), h > 2 }

A subscription service charges $10 for the first month and $8 for each subsequent month. Write a piecewise function to represent the total cost based on the number of months subscribed. How would you graph this function for up to 6 months?

• C(m) = {10, m = 1; 8m, m > 1}

• C(m) = {10, m = 1; 10 + 8(m - 1), m > 1}

• C(m) = {10 + 10(m - 1), m > 1}

• C(m) = {8m, m >= 1}