1. Section 5-3 Function Rules, Tables, and Graphs SPI 22H: select the linear graph that models the real-world situation SPI 52A: choose the matching linear graph given a set of ordered pair
Objectives: Model functions using rules, tables, and graphs
Vocabulary
Independent variable: x value (input, domain)
Dependent variable: y value (output, range)
Function Notation: f(x), h(c), y, g(a), etc.

2. Model a Function Rule by Graphing Model the function rule
y = ½ x + 3
Step 1. You choose input values for x unless specified.
Substitute into the equation to find y. x
independent
y = ½ x + 3
dependent
(x, y)
Ordered pair
y = ½ (0) + 3
= 3
(0, 3)
y = ½ (2) + 3
= 4 2
(2, 4)
y = ½ (-2) + 3
= 2 -2
(-2, 2)

3. Model a Function Rule by Graphing The line represents all
Step 2. Plot points on a coordinate plane using the ordered
pairs. 6 4 2 -2 -4 -6
(x, y)
Ordered pair
(0, 3)
The line represents all
x and y values that will
make the equation true.
(2, 4)
(-2, 2)
Step 3. Join points to form a line.

4. Real-world and Functions
At the local video store you can rent a video game for $3. It costs $5 a month to operate your video game player. The total monthly cost C(v) depends on the number of video games (v) you rent. Use the function rule C(v) = 5 + 3v to make a table of values and a graph.
Step 1. You choose input values for x unless specified.
Substitute into the equation to find y. x
independent
C(v) = 5 + 3v
Dependent
(x, y)
Ordered pair
C(v) = 5 + 3(0)
= 5
(0, 5)
C(v) = 5 + 3(5)
= 20 5
(5, 20)
C(v) = 5 + 3(8)
= 29 8
(8, 29)

5. Real-world and Functions (cont)
Step 2. Plot points using the ordered pair.
Choose appropriate intervals for units on the axes.
Given the problem there will be not negative values.
(x, y)
Ordered pair 45 35 40 30 20 25 15 5 10
(0, 5)
Rent 0 games, costs $5
(5, 20)
Total Cost
Rent 5 games, costs $20
(8, 29)
Rent 8 games, costs $29
Number of CDs

6. Graphs and their Equations
Linear Equation and its Graph
y = x + 2
Linear Equation:
equation has a variable with exponent no greater than 1
graph of the equation is a line
Increasing Function
(line goes up from left to right)
Decreasing Function
(line goes down from left to right)

7. Graphs and their Equations
Absolute Value Equation and its Graph
y = |x| + 2
Absolute Value:
equation has a variable that is an absolute value
graph of the equation is a V shape
Sign in front of the absolute value is positive
y = |x|
Sign in front of the absolute value is negative
y = - |x| + 2

8. Graphs and their Equations
Quadratic Equation and its Graph
y = x2 + 2
Quadratic Equation:
equation with a variable that has an exponent of 2
graph of the equation is a “U” shape
“U” shape is up when sign in front is positive
y = x2
“U” shape is down when sign in front is negative
y = - x2

9. Graph an Absolute Value Function Graph the function y = |x| + 2.
1. Create a table of values 6 4 2 -2 -4 -6 x
y = |x| + 1
(x, y)
y = |-2| + 1
= 3 -2
(-2, 3)
y = |-1| + 1
= 2 -1
(-1, 2)
y = |0| + 1
= 1
(0, 1)
y = |1| + 1
= 2 1
(1, 2)
y = |2| + 1
= 3 2
(2, 3)
2. Plot the ordered pair.
3. Connect with a V shape since it is a function of an absolute value.