Worksheet – Section 2.1
Name_______________________________
1. Let t  w2  16
a. Is a function of ? Explain your answer.
b. Is
a function of
Explain your answer.
2. Determine the domain of the following functions.
a. g ( x) 
1
x x
3
b. h(t )  3 t 2  1
c. r ( w) 
d.
3w
7w  9
 3  p
if p  2
f ( p)  
 5 p  3 if p  2
3. A 50-gallon tank is full. A pump is used to take water out of the tank at a rate of 5 gallons per
minute. After 6 minutes the pump is turned off and is immediately replaced with a pump that
removes water at a rate of 4 gallons per minute for 4 minutes.
Using a piecewise function, express the number of gallons of water in the tank after t minutes.
4. Solve each of the following equations for y , and determine if the equations represent
functions of x .
a.
b.
c.
5. Write an function for each of the following, using appropriate variable notation.
Interpret the horizontal and vertical intercepts, if applicable.
a) A machine with an initial value of $5,000 depreciates in value by $1000 per year. Let the
equation be the value after t years.
b) A boy who is 4 feet tall is growing at a rate of 2 inches per year. Let the equation be the
height of the boy after t years.
c) A person is paying $10 a week to a friend in order to pay back a $100 loan. Let the
equation be the amount the person still owes his friend after w weeks.
d) A rental car company charges $39 for a car, plus $.20 per mile driven. Let the equation
be the amount the customer pays when m miles are driven.