Functions and Equations
Glue
CCSS6.EE.9 Represent and analyze quantitative relationships between dependent
and independent variables.
Review: You can use an equation to represent a function. The input, or
independent variable, represents the x-value, and the output, or dependent
variable, represents the y-value. An equation expresses the dependent
variable in terms of the independent variable.
EXAMPLE: Write an equation to represent the function rule shown in the
table. Complete the rest of the function table.
Input, x
Output, y
Rule:
0
0
1
2
2
4
4
6
10
EXAMPLE: Write an equation to represent the function rule shown in the
table. Complete the rest of the function table.
Input, x
Output, y
Rule:
1
3
2
3
2
3
1
1
3
1
1
3
2
2
3
1
1
2
3
2
EXAMPLE: Write an equation to represent the function rule shown in the
table.
Rule:
Input, x
1
2
3
4
5
6
Output, y
4
6
8
10
12
14
You can also graph a function. If the graph is a line, the function is
then called a linear function.
Graph the equation _________________________________ in your Journal.
Step 1: List the ordered pairs from the table. (input, output)
(x, y)
Step 2: Graph each ordered pair. Draw a line through each point.
Babysitting The table shows the amount of money Carli earns based on
the number of hours she babysits.
Hours Babysitting
Earnings ($)
1
6
2
12
3
18
4
24
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
Write a sentence that describes the relationship between the
number of hours she babysits and her earnings. _______________
_______________________________________________________
_______________________________________________________
Does she earn the same amount each hour? ____________ Explain.
_______________________________________________________
_______________________________________________________
What is the function rule for the table? _______________________
What are the independent variables? _________________________
What are the dependent variables? __________________________
State the domain. ________________________________________
State the range. __________________________________________
What represents the x-axis? ________________________________
What represents the y-axis? ________________________________
Create a line graph for the function table in your Journal. Use your
ruler!!
Satellite TV A company charges $50 per month for satellite television
service plus an additional $5 for each movie ordered. The equation y=50+5x
describes the total amount y a customer will pay if they order x movies.
Graph the function in your Journal.
Step 1: Create a function table for the equation (rule). Make a list
of the ordered pairs. Select any three or four values for x. Substitute these
values for x to find y.
Step 2: Graph each ordered pair. Draw a line through each point.
Fair A fair charges an admission fee of $8.
Each ride is an additional $2. The equation
t = 8 + 2r describes the total charge t for the
number of rides r. Graph the function.
Car Wash The Student Council is holding a car wash to raise money. They
are charging $7 for each car they wash.
Write an equation and make a function table to show the
relationship between the number of cars washed c and the total amount
earned t.
Rule:
Graph the equation in your Journal. Use your ruler. Is this equation
a linear equation? ________________
CHECK EACH OF YOUR GRAPHS FOR REQUIRED ELEMENTS.
Did you give the graph an appropriate title?
Did you identify the horizontal axis as x and the vertical
axis as y?
Did you label the x and y axis?
Did you create equal intervals for your scales?
Did you measure equal spacing for the intervals?
Did you plot the ordered pairs accurately?
Did you connect your points with a line?