Analyzing Piecewise Functions: Cost and Behavior Insights

A taxi company charges a flat fee of $3 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) = { 3 + 2x, if x <= 1; 5 + 2(x - 1), if x > 1. Domain: [0, ∞), Range: [5, ∞)

• C(x) = { 3, if 0 < x <= 1; 3 + 2(x - 1), if x > 1. Domain: (0, ∞), Range: [3, ∞)

• C(x) = { 2x, if x <= 1; 3 + 2(x - 1), if x > 1. Domain: (0, ∞), Range: [2, ∞)

• C(x) = { 3, if x = 1; 3 + 3(x - 1), if x > 1. Domain: (0, 1], Range: [3, 6)

A gym charges a monthly fee of $30, plus $5 for each class attended. Create a step function to model the total cost based on the number of classes attended. What is the domain and range of this function?

• Domain: n >= 0; Range: C < 0

• Domain: n >= 0; Range: C >= 30

• Domain: n <= 0; Range: C = 30

• Domain: n > 0; Range: C < 30

A delivery service charges $10 for the first 5 miles and $1 for each additional mile. Write a piecewise function for the total cost of delivery and analyze its behavior as the distance increases.

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

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

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

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

A concert ticket costs $50 for the first 100 tickets sold, and $75 for any tickets sold after that. Define a piecewise function for the ticket price based on the number of tickets sold. What is the domain and range?

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

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

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

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

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 total cost based on data usage. Determine the domain and range of this function.

• C(x) = { 15, 0 <= x <= 500; 15 + 0.05(x - 500), x > 500 } with domain [0, 1000) and range [15, 100)

• C(x) = { 25, 0 <= x <= 500; 25 + 0.20(x - 500), x > 500 } with domain [0, ∞) and range [25, ∞)

• C(x) = { 20, 0 <= x <= 500; 20 + 0.10(x - 500), x > 500 } with domain [0, ∞) and range [20, ∞)

• C(x) = { 20, 0 <= x <= 300; 20 + 0.10(x - 300), x > 300 } with domain [0, ∞) and range [20, 100)

A parking garage charges $5 for the first hour and $2 for each additional hour. Create a step function to represent the total parking fee based on the number of hours parked. What is the domain and range?

• Domain: [0, 10], Range: [0, 10)

• Domain: [0, ∞), Range: [0, ∞)

• Domain: [1, ∞), Range: [5, 20]

• Domain: [0, ∞), Range: [5, ∞)

A subscription service charges $10 for the first month and $5 for each subsequent month. Write a piecewise function to model the total cost over time. Analyze the function behavior as the number of months increases.

• C(m) = { 10, m = 1; 5m + 2, m > 1 }

• C(m) = { 10, m = 1; 5m + 5, m > 1 }

• C(m) = { 10, m = 1; 10m - 5, m > 1 }

• C(m) = { 5m, m = 1; 5m + 10, m > 1 }

A water utility company charges a base fee of $15 for the first 1000 gallons and $0.02 for each additional gallon. Define a piecewise function for the water bill and determine its domain and range.

• B(x) = { 10, if 0 ≤ x ≤ 1000; 10 + 0.03(x - 1000), if x > 1000; Domain: [0, 2000), Range: [10, 200)

• B(x) = { 15, if 0 ≤ x ≤ 500; 15 + 0.05(x - 500), if x > 500; Domain: [0, ∞), Range: [15, ∞)

• B(x) = { 20, if 0 ≤ x ≤ 1000; 20 + 0.01(x - 1000), if x > 1000; Domain: [0, ∞), Range: [20, ∞)

• B(x) = { 15, if 0 ≤ x ≤ 1000; 15 + 0.02(x - 1000), if x > 1000; Domain: [0, ∞), Range: [15, ∞)

A delivery service charges $5 for the first 3 miles and $1.50 for each additional mile. Write a piecewise function for the delivery cost and analyze how the cost changes with distance.

• C(d) = { 5, if 0 <= d <= 3; 10 + 1.5 * (d - 3), if d > 3 }

• C(d) = { 5, if 0 <= d <= 3; 5 + 1.5 * (d - 3), if d > 3 }

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

• C(d) = { 5, if d < 0; 5 + 2 * (d - 3), if d >= 3 }

A school charges $100 for the first 10 students and $80 for each additional student for a field trip. Create a piecewise function to represent the total cost based on the number of students. What is the domain and range of this function?

• C(n) = { 100, n < 1; 100 + 80(n - 10), n ≤ 10 } with domain n ∈ [0, 10] and range C(n) ∈ [0, 100)

• C(n) = { 100, 1 ≤ n ≤ 10; 100 + 80(n - 10), n > 10 } with domain n ∈ [1, ∞) and range C(n) ∈ [100, ∞)

• C(n) = { 100, 1 ≤ n ≤ 15; 100 + 80(n - 15), n > 15 } with domain n ∈ [1, 20] and range C(n) ∈ [100, 200)

• C(n) = { 100, 1 ≤ n ≤ 10; 100 + 80(n - 10), n ≥ 10 } with domain n ∈ [1, 15] and range C(n) ∈ [100, 500)