Name: Date:
6.2 Representing Functions
Objective: Represent a function in different forms
Represent a function as an algebraic equation, a table, and a graph.
Example 1: A tank contains 8 gallons of water. Water is then pumped into the tank at a rate of 2 gallons per minute. The total amount of water in the tank, y gallons, is a function of the number of minutes, x, that water has been pumped into the tank.
a) Write a verbal description of the function. Then write an algebraic equation for the function.
b) Construct a table of c) Use the table of values to
x- and y-values for the function. plot a graph to represent the function.
x / y1
2
3
Try this with your partner…
1. A game shop rents our video games at a rate of $6 per game. The total amount of money the shop collect, y dollars, is a function of the number of games, x, that the shop rents out.
a) Write an algebraic equation for the function.
b) Construct a table of c) Use the table of values to
x- and y-values for the function. plot a graph to represent the function.
x / y1
2
3
Try this one on your own…
2. A fire sprinkler sprays water at a rate of 8 gallons per minute. The total of water being sprayed, y gallons, is a function of the number of minutes, x, that the shop rents out.
a) Write an algebraic equation for the function.
b) Construct a table of c) Use the table of values to
x- and y-values for the function. plot a graph to represent the function.
x / y1
2
3
Translate a table of values for a function into a graph and an algebraic equation.
Example 2: Rachel starts cycling a distance away from her house at a constant rate. The table shows her distance from home, y meters, as a function of the time she takes to cycle, x seconds.
a) Graph the function. Use 1 unit on
the horizontal axis for the x interval
0 to 5, and 1 unit on the vertical axis
to represent 4 meters for the y interval
from 6 to 26.
Try this with your group…
Example 2: The table shows the total distance, y miles, indicated on the odometer of Jason’s car and the amount of gasoline used, x gallons, on a particular day.
a) Graph the function. Use 1 unit on
the horizontal axis for the x interval
0 to 5, and 1 unit on the vertical axis
to represent 30 miles for the y interval
from 1,000 to 1,150.