Transcript Lesson 3.1

Lesson 3.1
Objectives:
Vocabulary:
EQ: What is a function?
Identifying functions, Finding Domain and Range and
identifying independent and dependent variables.
Function – is a rule or math problem that shows a relationship between
two quantities.
Input – is the independent variable also called the domain. The input is the
x –value.
Output – is a dependent variable and the solution to the function and is
also called the range. The range is the y-value.
y=x+5
Example: A sample Input Output table:
The first (left) column is the input (domain)
Independent variable.
The second (right) column is the output (range)
Dependent variable.
Input x output y
0
5
1
6
2
7
3
8
Functions: For a function to exist, it must be true that for each input
there is exactly one output. (The input (x) does not repeat)
Examples:
a) Student ID #’s do not repeat. No students have the same ID#.
b) Phone numbers do not repeat. Two different homes do
not have the same number.
Decide if the following tables represent a function
input
output
input
output
1
2
3
4
5
8
11
14
1
2
2
3
4
5
6
7
Yes a function
Not a function
input
1
2
3
4
output
5
5
5
5
Yes a function
Relation – a rule that associates more than one output with an
input. A relation is defined to be any set of ordered pairs.
Vertical Line Test
A relation is a function if and only if no vertical line passes through
two or more points on the graph.
Function
Not a Function
Function
Not a Function. A vertical
line can be drawn through
two points
Determine the range of y = 2x +5 when the
domain is 0, 1, 2, 3 and 4
Domain
Range
0
1
2
3
4
Range is 5, 7, 9, 11and 13
Find the domain and the range of the function
Domain: Continuous change in x
Range: Continuous change in y
-2 < x < 3
-1 < y < 2
The dependent variable depends on the value of the
independent variable. When an equation represents a
function, the dependent variable is defined in terms of the
independent variable. The statement “y is a function of x”
means that y varies depending on the value of x.
The function y = −3x + 12 represents the amount
y (in fluid ounces) of juice remaining in a bottle
after you take x gulps.
y is dependent variable. It depends on x (independent variable)
Fluid remaining
# of gulps