Transcript 5-3 PPT Rules Tables and Graphs

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.
Model a Function Rule by Graphing
Model the function rule
y=½x+3
Step 1. You choose input values for x unless specified.
Substitute into the equation to find y.
x
y=½x+3
(x, y)
independent
dependent
Ordered pair
0
2
-2
y = ½ (0) + 3
=3
y = ½ (2) + 3
=4
y = ½ (-2) + 3
=2
(0, 3)
(2, 4)
(-2, 2)
Model a Function Rule by Graphing
Step 2. Plot points on a coordinate plane using the ordered
pairs.
6
(x, y)
Ordered pair
4
(0, 3)
2
(2, 4)
(-2, 2)
-7 -6 -5
-4 -3 -2 -1
0
-2
-4
-6
Step 3. Join points to form a line.
1 2
3
4
5
6
7
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
C(v) = 5 + 3v
(x, y)
independent
Dependent
Ordered pair
0
5
8
C(v) = 5 + 3(0)
=5
C(v) = 5 + 3(5)
= 20
C(v) = 5 + 3(8)
= 29
(0, 5)
(5, 20)
(8, 29)
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)
(0, 5)
Rent 0 games, costs $5
(5, 20)
Rent 5 games, costs $20
(8, 29)
Rent 8 games, costs $29
Total Cost
Ordered pair
45
40
35
30
25
20
15
10
5
0
0 1 2 3 4 5 6 7 8 9
Number of CDs
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)
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
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
Graph an Absolute Value Function
Graph the function y = |x| + 2.
1. Create a table of values
6
x
y = |x| + 1
(x, y)
-2
y = |-2| + 1
=3
y = |-1| + 1
=2
y = |0| + 1
=1
y = |1| + 1
=2
y = |2| + 1
=3
(-2, 3)
4
(-1, 2)
2
-1
0
1
2
(0, 1)
-7 -6 -5
-4 -3 -2 -1
0
1 2
3
4
5
(1, 2)
-2
(2, 3)
-4
2. Plot the ordered pair.
-6
3. Connect with a V shape since it is a function of an absolute value.
6
7