A.4.5 Practice Problems
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.
a. Write a sentence describing the meaning of the statement C(2)=40.
b. Which is less, C(4) or D(4)? What does this mean for the two phone plans?
c. Which is less, C(5) or D(5)? Explain how you know.
d. For what number g is C(g)=130?
e. 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)?
Problem 3
Function P gives the perimeter of an equilateral triangle of side length s. It is represented by the equation P(s)=3s.
a. What does P(s)=60 mean in this situation?
b. 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.
a. Describe the meaning of G(Jada)=4.
b. Find the value of G(Diego).
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.
a. W(2)=5
b. W(6)>W(4)
c. W(12)=W(15)
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:
a. Explain what each equation or inequality represents.
b. His mom says he should also include the inequality f>0. Do you agree? Explain your reasoning.