# Lesson 11

Domain and Range (Part 2)

The practice problem answers are available at one of our IM Certified Partners

### Problem 1

A child tosses a baseball up into the air. On its way down, it gets caught in a tree for several seconds before falling back down to the ground.

Select the best description of the range of this function.

A:

The range includes all numbers from 5 to 12.5.

B:

The range includes all integers between 0 and 12.5.

C:

The range includes all numbers from 0 to 8.5.

D:

The range includes all numbers from 0 to 12.5.

To raise funds for a trip, members of a high school math club are holding a game night in the gym. They sell tickets at \$5 per person. The gym holds a maximum of 250 people. The amount of money raised is a function of the number of tickets sold. Which statement accurately describes the domain of the function? A: all numbers less than 250 B: all integers C: all positive integers D: all positive integers less than or equal to 250 ### Problem 3 $$C$$ 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? (From Algebra1, Unit 4, Lesson 5.) ### Problem 4 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. Match each description with a graph that could represent it. ### Problem 5 The graph $$H$$ shows the height, in meters, of a rocket $$t$$ seconds after it was launched. 1. Find $$H(0)$$. What does this value represent? 2. Describe the domain of this function. 3. Describe the range of this function. 4. Find $$H(x) = 0$$. What does this value represent? ### Problem 6 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 under plan A.
2. Write an equation for function $$B$$, which gives the cost, in dollars, of buying $$n$$ meals under plan B.
3. Mai estimates that she’ll buy 15 meals per month. Which meal plan should she choose? Explain your reasoning.
(From Algebra1, Unit 4, Lesson 5.)

### Problem 7

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.
(From Algebra1, Unit 2, Lesson 25.)