Download Ch. 3 * Perpendicular and Parallel Lines

1.2 – Functions and Graphs
Function = A set of ordered pairs that has each
input (x) giving exactly one output (y)
X
Y
X
Y
 Ex:

-2
3
5
3
0
4
0
4
8
32
8
32
7
5
5
-6
Function
Not a function;
One input gives 2 outputs
Domain = the set of all inputs (x)
 Range = the set of all outputs (y)




Ex: A = πr2 . What is the range and domain?
 Domain = set of all r’s…
 Since r can’t be negative, domain is r≥0
 Range = set of all A’s
 Since r≥0, we know A won’t be negative, so range is A≥0
Ex: When using a number line, there is no range, only domain.
Write the following domains. The red line represents the domain.
-5
0
5
All real numbers
-5
0
5
x0
(0, )
-5
0
5
You must know both notations!
x
(, )
x2
(, 2]

Ex: When using a number line, there is no range, only domain.
Write the following domains. The red line represents the domain.
-5
-5
0
0
5
5
x  2
(, 2), (2, )
x  5 or x  0
(, 5], (0, )
-5
0
5
4  x  2
[4, 2]
-5
0
5
x  2 or 4  x  8
(, 2], (4,8)

Ex: Find the domains and ranges of each graphed function.

Assume all real numbers unless the graph DOESN’T exist for a certain value

Hint: Look for asymptotes, holes, and blank sections of the graph!

Use parenthetical notation!

Domain:
Range:







(, )
[0, )
Domain: (, 0), (0, )
Range: (, 0), (0, )
y  x2
y
1
x
Domain: [0,  )
Range: [0,  )
y x
Domain: [2, 2]
Range: [0, 2]
y  4  x2

A function is even if it is symmetric
about the y-axis (flip it over the y-axis
and it’s the same!)
 f(-x) = f(x)

A function is odd if it is symmetric
about the origin (turn it upside-down
and it’s the same!)
 f(-x) = -f(x)

A graph symmetric about the x-axis
is…
 …not a function!