# Lesson 5

Using Function Notation to Describe Rules (Part 2)

Let’s graph and find the values of some functions.

The cell phone plan from Company C costs $10 per month, plus$15 per gigabyte for data used. The plan from Company D costs $80 per month, with unlimited data. Rule $$C$$ gives the monthly cost, in dollars, of using $$g$$ gigabytes of data on Company C’s plan. Rule $$D$$ gives the monthly cost, in dollars, of using $$g$$ gigabytes of data on Company D’s plan. 1. Write a sentence describing the meaning of the statement $$C(2) = 40$$. 2. Which is less, $$C(4)$$ or $$D(4)$$? What does this mean for the two phone plans? 3. Which is less, $$C(5)$$ or $$D(5)$$? Explain how you know. 4. For what number $$g$$ is $$C(g) = 130$$? 5. Draw the graph of each function. ### Problem 2 Function $$g$$ is represented by the graph. For what input value or values is $$g(x)=4$$? A: 2 B: -2 and 2 C: 16 D: none ### Problem 3 Function $$P$$ gives the perimeter of an equilateral triangle of side length $$s$$. It is represented by the equation $$P(s)=3s$$ 1. What does $$P(s)=60$$ mean in this situation? 2. Find a value of $$s$$ to make the equation $$P(s)=60$$ true. ### Problem 4 Function $$G$$ takes a student’s first name for its input and gives the number of letters in the first name for its output. 1. Describe the meaning of $$G(\text{Jada})=4$$. 2. Find the value of $$G(\text{Diego})$$. (From Unit 4, Lesson 2.) ### Problem 5 $$W$$ gives the weight of a puppy, in pounds, as a function of its age, $$t$$, in months. Describe the meaning of each statement in function notation. 1. $$W(2)=5$$ 2. $$W(6)>W(4)$$ 3. $$W(12)=W(15)$$ (From Unit 4, Lesson 3.) ### Problem 6 Diego is building a fence for a rectangular garden. It needs to be at least 10 feet wide and at least 8 feet long. The fencing he uses costs$3 per foot. His budget is \$120.

He wrote some inequalities to represent the constraints in this situation:

$$f=2x+2y$$​​​​​​

$$x \geq 10$$

$$y \geq 8$$

$$3f \leq 120$$

1. Explain what each equation or inequality represents.
2. His mom says he should also include the inequality $$f >0$$. Do you agree? Explain your reasoning.
(From Unit 2, Lesson 18.)