2.1 – Represent Relations and
Functions.
A relation is a mapping or pairing of input
values with output values. The set of input
values is the domain and the set of output
values is the range.
2.1 – Represent Relations and
Functions.
2.1 – Represent Relations and
Functions.
Example 1:
Consider the relation given by the ordered
pairs (-2, -3), (-1, 1), (1, 3), (2, -2), and
(3, 1)
a. Identify the domain and range.
b. Represent the relation using a graph and
a mapping diagram.
2.1 – Represent Relations and
Functions.
A function is 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.
2.1 – Represent Relations and
Functions.
Example 2:
Tell whether the relation is a function.
Explain.
2.1 – Represent Relations and
Functions.
You can use the graph of a relation to
determine whether it is a function by
applying the vertical line test.
2.1 – Represent Relations and
Functions.
2.1 – Represent Relations and
Functions.
Many functions can be described by an
equation in two variables, such as
y = 3x – 5. The input variable (in this
case, is x) is called the independent
variable (domain). The output variable
(in this case, y) is called the dependent
variable (range) because its value
depends on the value of the input variable.
2.1 – Represent Relations and
Functions.
2.1 – Represent Relations and
Functions.
Example 4: Graph the equation
y = -2x - 1
2.1 – Represent Relations and
Functions.
The function y = -2x – 1 in Example 4 is a
linear function because it can be written in the
form y = mx + b where m and b are
constants. The graph of a linear function is a
line. By renaming y as f(x), you can write y
=mx + b using function notation.
y = mx + b
f(x) = mx + b
2.1 – Represent Relations and
Functions.
Example 5:
Tell whether the function is linear. Then
evaluate the function when x = -4.
a. f(x) = -x2 – 2x + 7
b. g(x) = 5x + 8
2.1 – Represent Relations and
Functions.