Word Problems
Challenge: Evaluating Functions
Independent & Dependent
Linear/Nonlinear
Is it a Function?
100
For babysitting, Nicole charges a flat fee of $3, plus $5 per hour. Write an equation for the cost, C, after h hours of babysitting.
C = 5h + 3
100
Evaluate f(2) if f(x)=-3x
f(2) = -6
100
You and a friend are studying for a quiz. You want to get a higher score than your friend, so you decide to spend exactly 20 more minutes studying than your friend does. The relationship between these two variables can be expressed by the equation y=f+20, where f is the number of minutes your friend spends studying, and y is the number of minutes you spend studying. Identify the independent and dependent variables.
Independent Variable: The number of minutes your friend spends studying. Dependent Variable: The number of minutes you spend studying.
100
Linear or Nonlinear? Explain why.
y = -7/x
Nonlinear because there is an x in the denominator
100
Is it a function? Justify your answer.
{(2, 3), (4, 5), ( -2, 6)}
Yes, each input has exactly one output.
200
Rufus collected 100 pounds of aluminum cans to recycle. He plans to collect an additional 25 pounds each week. Write the equation for the total pounds, P, of aluminum cans after w weeks.
P = 25w + 100
200
Evaluate f(7) if f(x)= -(4x+2)
f(7) = -30
200
Identify the independent variable: The relationship between the number of hours worked and the amount of money earned.
The number of hours worked.
200
Linear or Nonlinear? Explain why.
y = -2x + 12
Linear because there are no exponents with a power other than 1
200
Using the vertical line test, does the graph of the points (1,3) and (1,5) represent a function?
No, the points fail the Vertical Line Test.
300
A canoe rental service charges a $20 transportation fee and $30 dollars an hour to rent a canoe. What is the cost of renting the canoe for 6 hours?
$200
300
Evaluate f(-6) if f(x)=x^2 - 9
f(-6) = 27
300
Identify the dependent variable: The relationship between your allowance and the number of chores you do.
Your allowance.
300
Is the graph linear or nonlinear? 
Nonlinear
300
Is it a function? Justify your answer.
| x | y |
| 2 | 4 |
| 1 | 5 |
| 2 | 6 |
No, the input of 2 has two different outputs.
400
Suppose that the water level of a river is 34 feet and that it is receding at a rate of 0.5 feet per day. Write an equation for the water level, L, after d days. In how many days will the water level be 26 feet?
16 days
400
Evaluate f(x)=9 if f(x)=25 - 4x
x = 4
400
Identify the independent and dependent variables: You are buying boxes of cookies at a bakery. Each box of cookies costs $4.
Independent Variable: The number boxes of cookies purchased.
Dependent Variable: How much you spend at the bakery.
400
Linear or Nonlinear? Explain why.
(0,1)
(1,3)
(2,5)
(3,7)
Linear because x values are increasing by 1 as y values are increasing by two; it is a constant rate of change
400
Is it a function? Justify your answer.
Yes, it passes the Vertical Line Test.
500
A caterer charges $120 to cater a party for 15 people and $200 for 25 people. How much would a party for 40 people cost?
$320
500
Evaluate f(x)=42 if f(x)=3x^2+15
x = 3 or -3
500
Identify the independent and dependent variables: On your math quiz, you earn 5 points for each question that you answer correctly.
Independent Variable: Number of questions answered correctly. Dependent Variable: Score on the quiz.
500
Linear or Nonlinear? Explain why.
(-5, 1), (-3, 2), (-1, 4), (1, 7), (3, 11), (5, 16)
Nonlinear because x values are increasing by 2 while y values are not increasing consistently; it is not a constant rate of change
500
Is it a function? Justify your answer. 
Yes, each input has exactly one output; it passed the vertical line test