1. Ch. 1 – PREREQUISITES FOR CALCULUS
1.2 – Functions and Graphs

2. One input gives 2 outputs
Functions
Function = A set of ordered pairs that has each input (x) giving exactly one output (y)
Ex:
Domain = the set of all inputs (x)
Range = the set of all outputs (y) X Y -2 3 4 8 32 7 5 X Y 5 3 4 8 32 -6
Function
Not a function;
One input gives 2 outputs

3. Functions 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.
You must know both notations! 5 -5
All real numbers 5 -5 5 -5

4. Functions
Ex: When using a number line, there is no range, only domain. Write the following domains. The red line represents the domain. 5 -5 5 -5 5 -5 5 -5

5. Domain and range of 2D Graphs
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:

6. Functions
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!