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Section 8.2
1. What is the vertical line test for? How does it work?
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2. Which of these graphs represent a function?
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The graph of a function y = f(x) is the set of all points in the plane (x, f (x)) where x is any value from the domain and f (x) is the corresponding range value, or output.
(x, y) = ( _______, ________ )
To evaluate a function from the graph, locate the point on the graph having the given ________ as the ______ coordinate. The ________ coordinate of this point will be the desired function value.
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EX: Find:
f(2)
y
y = f(x)
f(0)
f(4)
f(−3)
x
For which values of x is f(x) = 3?
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INTERVAL NOTATION
An interval is a continuous segment of the number line.
Notation: [(a, b)]
Where the segment ___ on the _____
Where the segment ______ on the _____
* We always write an interval from left to right (negative towards positive) on the number line.
[ or ] means equality is _____________
( or ) means equality is _____________
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Graphing Notation:
means equality is ___________
means equality is ___________
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Write the interval using interval notation, and graph it on the number line.
{x | −7 < x ≤ 6}
­10 ­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
1
2
3
4
5
6
8
7
10
9
{x | x ≤ 4}
­5
­4
­3
­2
­1
0
1
2
3
4
5
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{x | x > −1/2}
­5
­4
­3
­2
­1
0
1
2
3
4
5
­1
0
1
2
3
4
5
{x | x is any real number}
­5
­4
­3
­2
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February 24, 2017
Write the interval using set­builder notation, and graph it on the number line.
[−6, 4)
­10 ­9
­8
­7
­6
­5 ­4
­3
­2
­1
0
1
2
4
3
6
5
7
8
9
10
[2, ∞)
­5
­4
­3
­2
­1
0
1
2
3
4
5
­5
­4
­3
­2
­1
0
1
2
3
4
5
(−∞, −3)
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February 24, 2017
9. Find the domain and range. Use interval notation.
D:
D:
D:
R:
R:
R:
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