Lesson 5

Using Function Notation to Describe Rules (Part 2)

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

Problem 1

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.

    Blank grid. Horizontal axis, 0 to 8, gigabytes of data used. Vertical axis, 0 to 160 by 10’s, dollar cost.

Problem 2

Function \(g\) is represented by the graph.

For what input value or values is \(g(x)=4\)?

Parabola on coordinate grid.



-2 and 2





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:


\(x \geq 10\)

\(y \geq 8\)

\(3f \leq 120\)

  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.)