1.1 Relations and Functions
1.1 Relations and Functions
1.1 Relations and Functions
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<strong>1.1</strong> <strong>Relations</strong> <strong>and</strong> <strong>Functions</strong><br />
A function is a set of ordered pairs in which each<br />
element of the domain is paired with exactly one<br />
element of the range.<br />
The domain of a function is a set of all the x<br />
coordinates of the relation.<br />
The range is the set of all the y coordinates of the<br />
relation.<br />
If a relation is a function, it must pass the<br />
vertical line test.<br />
Which means: If you draw a vertical line<br />
anywhere in the function <strong>and</strong> it intersects the<br />
graph in more than one point, then the<br />
relation is not a function.<br />
For example:<br />
This is not a function<br />
Is this a function?<br />
1
Ex.1<br />
State the domain <strong>and</strong> range.<br />
x<br />
y<br />
Is the relation a function?<br />
2 4<br />
3 5<br />
2 8<br />
3 9<br />
1 4<br />
Ex.2<br />
State the domain <strong>and</strong> range.<br />
Is the relation a function?<br />
2
Ex.3<br />
If f(x) = -2x 2 + 3x - 5<br />
Find<br />
a) f(5)<br />
b) f(m + 1)<br />
Ex.4<br />
State the domain of each function:<br />
3
Example 1<br />
Given f(x) = 2x 2 + 5 <strong>and</strong> g(x) = 3x 2, find each function.<br />
a. (f + g)(x)<br />
b. (f g)(x)<br />
c.<br />
d.<br />
x ≠ 2/3<br />
Honors Pre-Calc Homework:<br />
pg. 10 #38-45, 48-50, 53<br />
AND<br />
pg. 17 #11-12<br />
(for 11-12, write the domain after each operation)<br />
5
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