Download Chapter 2: Linear Equations and Functions

Chapter 2:
Linear Equations and Functions
Section 2.1:
Represent Relations and Functions
Relation – a mapping or pairing of input values
with output values.
Domain – the set of input values.
Range – the set of output values.
Function – a relation for which each input has
exactly one output.
*If any input of a relation has more than one
output, the relation is not a function.
Representing Relations
A relation can be represented in the following ways:
Ordered Pairs
(-2, 2), (-2, -2), (0, 1), (3, 1)
Table
x
y
-2
2
-2
-2
0
1
3
1
Graph
Mapping Diagram
Vertical Line Test
A relation is a function if and only if no vertical
line intersects the graph of the relation at more
than one point.
Equation in two variables – many functions can
be described by an equation in two variables,
such as y = 3x – 5.
Independent variable – the input variable (in
this case, x).
Dependent variable – the output variable (in
this case, y). It is called a dependent variable
because its value depends on the value of the
input variable.
Solution - an ordered pair (x, y) is a solution of
an equation in two variables if substituting x
and y in the equation produces a true
statement.
Graph – the graph of an equation in two
variables is the set of all points (x, y) that
represent solution of the equation.
Example 1:
Consider the relation given by (3, 2), (-1, 0),
(2, -1), (-2, 1), (0, 3).
a) Find the domain and range.
Domain: {-2, -1, 0, 2, 3}
Range: {-1, 0, 1, 2, 3}
b) Represent the relation using a mapping
diagram.
Example 2:
Is the relation a function? Explain.
a) (-5, 4), (-1, 0), (3, -1), (3, -2)
No
Input 3 has two different outputs.
b) (-3, 5), (0, 5), (2, 1), (6, -8)
Yes
Each input has exactly one output.
Example 3:
Use the vertical line test to tell whether the
relation is a function.
a)
b)
Yes
No
HOMEWORK (Day 1)
pg. 76 – 77; 3 – 23
Linear function – a function that can be written
in the form y = mx + b where m and b are
constants.
The graph of a linear function is a line.
Function notation – by renaming y as f(x), you
can write y = mx + b using function notation.
Domains in Real Life
The domain of a function is all real numbers
because there is an output for every real
number x.
In real life, you may need to restrict the domain
so that is reasonable in the given situation.
Graphing Equations in Two Variables
To graph an equation in two variables, follow
these steps:
1) Construct a table of values.
2) Plot enough points from the table to
recognize a pattern.
3) Connect the points with a line or a curve.
Example 4:
Tell whether the function is linear. Then
evaluate the function when x = -3.
a) f(x) = -2x3 + 5
Not linear
59
b) g(x) = 12 – 8x
Linear
36
HOMEWORK (Day 2)
pg. 78; 34 – 39
Example 5:
Graph the following equations.
a) y = 3x – 5
b) y = ½ x + 2
c) y = -4x – 1
HOMEWORK (Day 3)
pg. 77; 25 – 33