Transcript 2.3 Represent Relations and Functions

2.3
Represent Relations and
Functions
2.1-2.3 Quiz: FRIDAY
Vocabulary:
• A relation is a mapping, or pairing, of
input values with output values.
• The domain of a relation is the set of input
values (x-values)
• The range of a relation is the set of output
values (y-values).
• A function is a relation for which each
input value has exactly one output value.
 x-values CANNOT repeat!
Vocabulary
• Vertical Line Test
 By the 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.
More Vocabulary
• An equation in two variables has an independent
variable, and a dependent variable, that depends
on the value of the independent variable.
• An ordered pair (x, y) is a solution of an equation
in two variables if substituting x and y into the
equation produces a true statement.
• The graph of an equation in two variables is the
set of all points (x, y) that represent solutions of the
equation.
Yes….More Vocabulary
• A linear function can be written in the form
y = mx + b where m and b are constants, or
in function notation f(x) = mx + b.
• A function is one-to-one if no two values in
the domain have the same value in the
range.
 y-values CANNOT repeat for the function to be
one-to-one.
Example 1:
• Consider the relation given by the ordered
pairs (1, 0), (0, -2), (-2, 3), (3, 1)
 Identify the domain and range
 Represent the relation using a graph
 Use the vertical line test to tell whether the
relation is a function
 If the relation is a function, tell whether it is a
one-to-one function.
Example 1 Cont’d:
• D: -2, 0, 1, 3
R: -2, 0, 1, 3
• The relation IS a
function.
• The relation IS
one-to-one
Example 2:
• Graph the equation y = -2x – 2
Example 3:
•
Tell whether the function is linear. Then
evaluate the function when x = -3
a) f(x) = 6x + 10
b) g(x) = 2x2 + 4x – 1