Analyzing Piecewise Functions: Costs and Behaviors

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 total cost, and determine the domain and range of this function.

• C(x) = { 5, 0 < x <= 1; 5 + 2(x - 1), x >= 1; Domain: [0, 10), Range: [5, 25) }

• C(x) = { 5, 0 < x <= 1; 5 + 2(x - 1), x > 1; Domain: [0, ∞), Range: [5, ∞) }

• C(x) = { 5, 0 < x <= 2; 5 + 2(x - 2), x > 2; Domain: [0, ∞), Range: [5, 15) }

• C(x) = { 5, x < 0; 5 + 3(x - 1), x > 1; Domain: [0, 1), Range: [0, 10) }

A gym charges a monthly fee of $30 for the first three months, and then $20 for each subsequent month. Create a piecewise function for the total cost after 'x' months and analyze its behavior as 'x' increases.

• C(x) = { 30x, for x < 3; 90 + 30(x - 3), for x >= 3 }

• C(x) = { 30x, for 0 < x <= 3; 90 + 20(x - 3), for x > 3 }

• C(x) = { 30, for x <= 3; 60 + 20(x - 3), for x > 3 }

• C(x) = { 30, for x <= 3; 20(x - 3), for x > 3 }

A parking garage charges $10 for the first hour and $5 for each additional hour. Write a stepwise function to represent the total cost for parking and determine the domain and range of this function.

• C(t) = { 10, 0 < t <= 1; 10 + 5 * (t - 2), t > 1 } with domain t >= 0 and range C(t) >= 5.

• C(t) = { 10, 0 < t <= 1; 10 + 10 * (t - 1), t > 1 } with domain t >= 0 and range C(t) >= 10.

• C(t) = { 5, 0 < t <= 1; 5 * t, t > 1 } with domain t >= 0 and range C(t) >= 5.

• C(t) = { 10, 0 < t <= 1; 10 + 5 * (t - 1), t > 1 } with domain t >= 0 and range C(t) >= 10.

A delivery service charges $15 for the first 5 miles and $3 for each additional mile. Construct a piecewise function for the total delivery cost and analyze how the cost changes as the distance increases.

• C(d) = { 20, if 0 <= d <= 5; 20 + 4(d - 5), if d > 5 }

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

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

• C(d) = { 15, if 0 <= d <= 10; 15 + 5(d - 10), if d > 10 }

A concert ticket costs $50 for the first 100 tickets sold, and $75 for each ticket sold after that. Write a piecewise function to represent the ticket price based on the number of tickets sold and determine the domain and range.

• P(x) = { 50, for 0 <= x <= 100; 100, for x > 100 }. Domain: [0, ∞), Range: {50, 100}

• P(x) = { 50, for 0 <= x <= 150; 75, for x > 150 }. Domain: [0, ∞), Range: {50, 75, 100}

• P(x) = { 50, for 0 <= x <= 100; 75, for x > 100 }. Domain: [0, ∞), Range: {50, 75}

• P(x) = { 50, for 0 <= x <= 50; 75, for x > 50 }. Domain: [0, 100), Range: {50, 75}

A phone plan costs $25 for the first 500 MB of data and $10 for each additional 100 MB. Create a piecewise function for the total cost based on data usage and analyze its behavior as data usage increases.

• C(x) = { 30, 0 <= x <= 500; 30 + 15 * ceil((x - 500) / 100), x > 500 }

• C(x) = { 25, 0 <= x <= 500; 25 + 10 * ceil((x - 500) / 100), x > 500 }

• C(x) = { 20, 0 <= x <= 500; 20 + 5 * ceil((x - 500) / 100), x > 500 }

• C(x) = { 25, 0 <= x <= 400; 25 + 10 * ceil((x - 400) / 100), x > 400 }

A subscription service charges $10 for the first month and $5 for each month thereafter. Write a stepwise function to represent the total cost after 'x' months and determine the domain and range of this function.

• C(x) = { 10, x = 1; 5x + 5, x > 1; Domain: x >= 1; Range: C(x) >= 10.

• C(x) = 10x, x >= 1; Domain: x > 0; Range: C(x) >= 0.

• C(x) = 10 + 5x, x >= 1; Domain: x > 1; Range: C(x) >= 15.

• C(x) = 5x, x >= 1; Domain: x >= 1; Range: C(x) >= 5.

A water utility company charges a base fee of $15 for the first 1000 gallons and $0.02 for each additional gallon. Construct a piecewise function for the total bill based on water usage and analyze how the bill changes with increased usage.

• B(x) = { 15, if x < 1000; 15 + 0.02 * (x - 1000), if x >= 1000.}

• B(x) = { 15, if 0 <= x <= 1000; 15 + 0.02 * (x - 1000), if x > 1000.

• B(x) = { 15 + 0.02 * x, if x <= 1000; 15, if x > 1000.}

• B(x) = { 0, if 0 <= x <= 1000; 15 + 0.02 * (x - 1000), if x > 1000.}

A delivery service charges $20 for the first 10 miles and $4 for each additional mile. Write a piecewise function to represent the total delivery cost and determine the domain and range of this function.

• C(x) = { 15, 0 <= x <= 10; 15 + 5(x - 10), x > 10 } with domain [0, 20) and range [15, 30)

• C(x) = { 20, 0 <= x <= 5; 20 + 4(x - 5), x > 5 } with domain [0, ∞) and range [20, 80)

• C(x) = { 20, 0 <= x <= 10; 20 + 4(x - 10), x > 10 } with domain [0, ∞) and range [20, ∞)

• C(x) = { 25, 0 <= x <= 10; 25 + 3(x - 10), x > 10 } with domain [0, 50) and range [25, 100)

A cable company charges $50 for the first 100 channels and $1 for each additional channel. Create a piecewise function for the total cost based on the number of channels and analyze its behavior as the number of channels increases.

• C(x) = { 50, if x < 100; 50 + (x - 100), if x >= 100 }

• C(x) = { 50 + 2(x - 100), if x > 100; 50, if x <= 100 }

• C(x) = { 50 + (x - 50), if x <= 100; 50 + (x - 100), if x > 100 }

• C(x) = { 50, if x <= 100; 50 + (x - 100), if x > 100 }