Analyzing Continuity in Piecewise Functions: A Grade 11 Quiz

A delivery service charges $5 for the first 10 miles and $2 for each additional mile. Write a piecewise function to represent the cost of delivery based on the distance traveled. Determine if the function is continuous at 10 miles.

• The piecewise function is C(d) = {5, 0 <= d <= 10; 5 + 2(d - 10), d > 10}. The function is continuous at 10 miles.

• C(d) = {5, d < 10; 5 + 3(d - 10), d >= 10}. The function is discontinuous at 10 miles.

• C(d) = {10, 0 <= d <= 10; 10 + 2(d - 10), d > 10}. The function is continuous at 10 miles.

• C(d) = {5, 0 <= d <= 5; 5 + 2(d - 5), d > 5}. The function is continuous at 5 miles.

A water tank fills at a rate of 3 liters per minute for the first 15 minutes, then at 5 liters per minute for the next 10 minutes. Create a piecewise function for the volume of water in the tank over time. Analyze the behavior of the function at the 15-minute mark.

• V(t) = { 2t, 0 <= t <= 15; 30 + 4(t - 15), 15 < t <= 25 }

• V(t) = { 3t, 0 <= t <= 10; 30 + 5(t - 10), 10 < t <= 20 }

• V(t) = { 3t, 0 <= t <= 15; 45 + 5(t - 15), 15 < t <= 25 }

• V(t) = { 3t, 0 <= t <= 20; 60 + 5(t - 20), 20 < t <= 30 }

A parking garage charges $10 for the first hour and $2 for each additional hour. Write a piecewise function for the total cost of parking based on the number of hours parked. Determine if the function is continuous at 1 hour.

• The function is continuous at 1 hour.

• The cost is $12 at 1 hour.

• The function is only defined for 2 hours or more.

• The function is discontinuous at 1 hour.

A local gym has a membership fee of $30 per month for the first 6 months, and then it increases to $50 per month after that. Create a piecewise function to represent the total cost of membership over time. Analyze the function's behavior at the 6-month mark.

• C(t) = { 50t for 0 <= t <= 6, 30 + 30(t - 6) for t > 6 }

• C(t) = { 30t for 0 <= t <= 6, 30 + 50(t - 6) for t > 6 }

• C(t) = { 30t for 0 <= t <= 6, 180 + 50(t - 6) for t > 6 }

• C(t) = { 30 for 0 <= t <= 6, 50 for t > 6 }

A taxi company charges a flat fee of $3 for the first mile and $1.50 for each additional mile. Write a piecewise function for the fare based on the distance traveled. Determine if the function is continuous at 1 mile.

• The function is continuous only for distances greater than 1 mile.

• The function is continuous at 1 mile.

• The fare is $4.50 at 1 mile.

• The function is discontinuous at 1 mile.

A factory produces 100 units per day for the first 5 days, then increases production to 150 units per day for the next 5 days. Create a piecewise function to represent total production over the 10 days. Analyze the function's behavior at the 5-day mark.

• P(t) = {100t, 0 < t <= 5; 1000 + 100(t - 5), 5 < t <= 10}

• P(t) = {100t, 0 < t <= 5; 500 + 200(t - 5), 5 < t <= 10}

• P(t) = {150t, 0 < t <= 5; 500 + 100(t - 5), 5 < t <= 10}

• P(t) = {100t, 0 < t <= 5; 500 + 150(t - 5), 5 < t <= 10}

A cell phone plan costs $40 for the first 2 GB of data and $10 for each additional GB. Write a piecewise function for the monthly cost based on data usage. Determine if the function is continuous at 2 GB.

• The piecewise function is C(x) = { 40, 0 <= x <= 2; 40 + 10(x - 2), x > 2 } and it is continuous at 2 GB.

• C(x) = { 30, 0 <= x <= 2; 30 + 15(x - 2), x > 2 } and it is continuous at 2 GB.

• C(x) = { 40, 0 <= x <= 2; 50 + 10(x - 2), x > 2 } and it is discontinuous at 2 GB.

• C(x) = { 40, 0 <= x <= 2; 40 + 5(x - 2), x > 2 } and it is continuous at 2 GB.

A concert ticket costs $50 for the first 100 tickets sold and $75 for each ticket sold after that. Create a piecewise function for the total revenue based on the number of tickets sold. Analyze the function's behavior at the 100-ticket mark.

• R(x) = { 75x for 0 <= x <= 100, 5000 + 50(x - 100) for x > 100.

• R(x) = { 50x for 0 <= x <= 100, 10000 + 50(x - 100) for x > 100.

• R(x) = { 50x for 0 <= x <= 100, 5000 + 100(x - 100) for x > 100.

• R(x) = { 50x for 0 <= x <= 100, 5000 + 75(x - 100) for x > 100.

A subscription service charges $15 for the first 3 months and $10 for each month thereafter. Write a piecewise function for the total cost of the subscription over time. Determine if the function is continuous at the 3-month mark.

• C(t) = { 10, if 0 < t <= 3; 10(t - 3), if t > 3. Not continuous at t = 3.

• C(t) = { 15, if 0 < t <= 3; 15 + 5(t - 3), if t > 3. Continuous at t = 3.

• C(t) = { 15, if 0 < t <= 3; 15 + 10(t - 3), if t > 3. Continuous at t = 3.

• C(t) = { 15, if 0 < t <= 3; 20(t - 3), if t > 3. Continuous at t = 3.

A delivery service charges $4 for the first 5 miles and $1.50 for each additional mile. Create a piecewise function to represent the cost of delivery based on distance. Analyze the function's behavior at the 5-mile mark.

• C(d) = {4, for 0 <= d <= 5; 4 + 1 * (d - 5), for d > 5}

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

• C(d) = {4, for 0 <= d <= 10; 4 + 1.5 * (d - 10), for d > 10}

• C(d) = {4, for 0 <= d <= 5; 4 + 1.5 * (d - 5), for d > 5}