\(C\) gives the cost, in dollars, of a cafeteria meal plan as a function of the number of meals purchased, \(n\). The function is represented by the equation \(C(n)=4+3n\). 

1. Find a value of \(n\) such that \(C(n)=31\) is true. 
2. What does that value of \(n\) tell you about the cafeteria meal plan?

Lin completes a 5K using a combination of walking and running. Here are four graphs that represent four possible situations. Each graph shows the distance, in meters, as a function of time, in minutes.

Graph of piecewise function, origin O, no grid. Horizontal axis, time, minutes. Vertical axis, distance, meters. 4 sections. First section starts at origin and moves upwards and to the right, second section is steeper than first, third section is horizontal, fourth section is less steep than second.

Graph of piecewise function, origin O, no grid. Horizontal axis, time, minutes. Vertical axis, distance, meters. 4 sections. First section starts at origin and moves upwards and to the right, second section is less steep than first, third section is horizontal, fourth section is steepest.

Match each description with a graph that could represent it. 

The graph of \(H\) shows the height, in meters, of a rocket \(t\) seconds after it was launched.

1. Find \(H(0)\). What does this value represent?

   

   Function on coordinate plane, no grid, origin O. Horizontal axis, time, seconds, from 0 to 5. Vertical axis, height, meters, from 0 to 40 by 10’s. Line begins at 0 comma 15, curves upwards and to the right until 2 comma 35, decreasing until about 4 point 75 comma 0.

2. Describe the domain of this function.
3. Describe the range of this function.
4. Solve \(H(x) = 0\). What does this value represent?

Mai has to decide between two cafeteria meal plans. Under plan A, each meal costs \$2.50. Under plan B, one month of meals costs \$30.

1. Write an equation for function \(A\), which gives the cost, in dollars, of buying \(n\) meals in one month under plan A.
2. Write an equation for function \(B\), which gives the cost, in dollars, of buying \(n\) meals in one month under plan B.
3. Mai estimates that she’ll buy 15 meals per month. Which meal plan should she choose? Explain your reasoning.

Kiran is playing a video game. He earns 3 stars for each easy level he completes and 5 stars for each difficult level he completes. He completes more than 20 levels total and earns 80 or more stars.

1. Create a system of inequalities that describes the constraints in this situation. Be sure to specify what each variable represents.

2. Graph the inequalities and show the solution region.

   

3. Then, identify a point that represents a combination of stars and levels that is a solution to the system.
4. Interpret the point \((5,6)\) in the context of this situation and determine how many stars Kiran earns based on this point.