Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
Unit G ­ Day 1
Objectives:
1. Determine the domain and range of various types of functions.
2. Determine if a relation is a function using the Vertical Line Test
3. Create a graph from a given domain and range.
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Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
What is a function?
A function is a relation, or mapping, for
which each input has exactly one output.
Example 1:
Not a Function
Function
Input
-2
0
4
Output
4
7
9
Input
Output
-2
0
4
4
7
9
What makes the first mapping a
function and the second mapping not?
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Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
We will call the valid input values of a
function the domain and the resulting
output values the range.
In our previous example, the domain
consisted of the numbers -2, 0, 4 and
the range consisted of the numbers
4,7,9
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Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
Identify the Domain and Range of the following functions:
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Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
Example 2:
Graph each function and state the domain
and range.
a.) y = -5
D: ___________
R: ___________
b.) y = (x+3)(x-2)
D: ___________
R: ____________
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Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
Example 3:
Let's determine the domain and range of the following functions:
a.) f(x) = 3x2+ 5
b.) h(p) = √p ­3
D: ____ R: ____
D: _____ R: _____
c.) g(x)=x2 + 8
d.) h(w) = x3
x3
x2 + 8
D: _____ R: _____
D: _____ R: _____
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Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
If we have the graph of an equation, we can determine if the relation is a function by using the Vertical Line Test (VLT)
The Vertical Line Test tells us a relation is a function if and only if no vertical line intersects the graph of the relation at more than one point. 7
Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
Example 4: Determine if the following relations are functions using the VLT. Identify the Domain and Range.
D: ____ R: ____
D: ____ R: ____
D: ____ R: ____
D: ____ R: ____
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Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
Example 5:
Draw a graph that has the given domain and range.
a.)
D: (­2, 5)
R: [4,7]
b.)
D: all Real #s
R: y>5
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Day 1 ­ Domain and Range, VLT.notebook
October 15, 2014
Assignment: Worksheet
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