Warm up
What is the solution of :
1) 2𝑥 + 1 − 4 = 3𝑥
X = -1
Why is there only one answer?
2) Explain why the equation 7𝑥 + 2 = −11 has no solution.
An absolute value will NEVER be negative.
Unit 2
2-1
Relations and Functions
Functions, Equations and Graphs
Unit Objectives:
•
•
•
Identify and use different forms of linear
equations
Identify and use transformations on graphs and
equations/functions
Model real-life situations with linear functions.
Today’s Objective:
I can graph relations and identify functions.
Relations:
Mapping
Diagram
Input Output
-3
3
4
4
-1
-1
3
a set of input and output values
Table of
values
Ordered pairs
(input, output)
(x, y)
Input Output
(-3, 4)
x
y
(3, -1)
(4, -1)
-3
4
(4, 3)
3
4
4
-1
-1
3
Graphing
Domain:
Set of all input values
(x values)
Range:
Set of all output values
(y values)
{(-3, 14), (0, 7), (2, 0), (9, -18), (23, -99)}
Function: Each input has exactly one output
Domain Range
-3
0
4
-2
1
7
Function
Not a
Function
{(-7, 14), (9, -7),
(14, 7), (7, 14)}
Function
Function
Not a
Function
Function Rule: An equation that represents a function
𝒚 = 3𝒙 + 2
Output
Dependent
variable
Input
Independent
variable
𝒇(𝒙) = 3𝒙 + 2
Read:
f of x
p. 65:10-24
Evaluate the function for x = 4
𝒇 𝒙𝟒 = 3(𝟒)
3𝒙 + 2
𝒇(𝟒) = 14
(4,14)
𝒈 𝒙 = −4𝒙 + 1
for 𝑥 = −3
𝒈 −𝟑 = −4(−𝟑) + 1
𝒈(−𝟑) = 13 (-3,13)