tell whether the pairing is a function. identify a function example 2 a. a. the pairing is not a...
TRANSCRIPT
Tell whether the pairing is a function.
Identify a functionEXAMPLE 2
a.
The pairing is not a function because the input 0 is paired with both 2 and 3.
b.
Identify a functionEXAMPLE 2
OutputInput
21
0 0
4 8
6 12
The pairing is a function because each input is pairedwith exactly one output.
SOLUTION
GUIDED PRACTICE for Example 2
Tell whether the pairing is a function.
1221Output
12963Input2.
369
12
1221
The pairing is a function because each input is pairedwith exactly one output.
SOLUTION
GUIDED PRACTICE for Example 2
Tell whether the pairing is a function.
3210Output
7422Input3.
The pairing is not a function because each input is notpaired with exactly one output.
2
47
0123
SOLUTION
GUIDED PRACTICE for Example 1
1. Identify the domain and range of the function.
Input 0 1 2 4Output 5 2 2 1
The domain is the set of inputs: 0, 1, 2, and 4
The range is the set of outputs: 1, 2, and 5
Write a function ruleEXAMPLE 4
Write a rule for the function. Input
Output 2
1
6 123
4
8
60 10
SOLUTION
and let y or dependent variable. Notice that eachbe the output,
Let x be the input, or independent variable,
output is 2 more than the corresponding input. So, a rule for the function is y = x + 2.
Write a function rule for a real-world situationEXAMPLE 5
Concert Tickets
You are buying concert tickets that cost $15 each. You can buy up to 6 tickets. Write the amount (in dollars) you spend as a function of the number of tickets you buy.Identify the independent and dependent variables.Then identify the domain and the range of the function.
Write a function rule for a real-world situationEXAMPLE 5
SOLUTION
So, the function rule is A = 15n. The amount spent depends on the number of tickets bought, so n is the independent variable and A is the dependent variable.
Write a verbal model. Then write a function rule. Let n represent the number of tickets purchased and A represent the amount spent (in dollars).
A 15 n=
Amount spent
(dollars)
Cost per ticket
(dollars/ticket)
Tickets purchased
(tickets)= •
Write a function rule for a real-world situationEXAMPLE 5
Because you can buy up to 6 tickets, the domain of the function is 0, 1, 2, 3, 4, 5, and 6. Make a table to identify the range.
Amount (dollars), A
0 1 32 654
0 15 4530 7560 90
Number of tickets, n
The range of the function is 0, 15, 30, 45, 60, 75, and 90.
Graph a function
EXAMPLE 1
STEP 2 Plot a point for each ordered pair (x, y).
STEP 2
Plot the points
EXAMPLE 2Graph a function
Replacement Set
• {0,1,2,5} is the replacement set for inputs for f(x)=2x+1
• What is the replacement set for outputs?
Evaluate Functions
• Evaluate f(x)=x2+1 for • f(4)• F(10)
Linear vs. Quadratic
• Graphs as a _____• Power of x is ___• _____is constant
• Graphs as a _____• Power of x is _____• _____ is not constant
but is changing at a constant rate
Linear vs. Quadratic
inputs outputs
0 15
1 21
2 27
3 33
4 39
5 45
x
Inputs outputs
0 5
1 6
2 9
3 14
4 21
5 30
x
Is it linear, quadratic or neither?
inputs outputs
0 -2
1 -1
2 2
3 7
4 14
inputs outputs
0 4
1 2
2 -4
3 -6
4 -10
inputs outputs
0 -5
1 -4
2 -1
3 0
4 1
inputs outputs
0 -1
1 4
2 9
3 14
4 19
inputs outputs
0 9
1 10
2 13
3 18
4 25
inputs outputs
0 7
1 5
2 3
3 1
4 -1
RESET CALCULATOR
• GO TO MEMORY (2ND THEN +)
• SELECT RESET (7)• ALL RAM (1)• RESET (2)
How to plot points on calculator
• Enter Data into Lists
• Turn Stat Plot On
• Window or ZoomStat
• Calculator goes here
Linear Regression
• Press STAT• Go To CALC• Select 4 for linear
regression• Press Enter• Input into y=• Graph
Quadratic Regression
• Press STAT• Go To CALC• Select 5 for quadratic
regression• Press Enter• Input into y=• Graph