1. 2.1 Functions

2. Let X and Y be two nonempty sets of real numbers
Let X and Y be two nonempty sets of real numbers. A function from X into Y is a rule or a correspondence that associates with each element of X a unique element of Y.
The set X is called the domain of the function.
For each element x in X, the corresponding element y in Y is called the image of x. The set of all images of the elements of the domain is called the range of the function.

3. f x y x y x X Y
RANGE
DOMAIN

4. Determine which of the following relations represent functions.
Not a function.
Function.
Function.

5. Not a function.
(2,1) and (2,-9)both work.

6. Find the domain of the following functions:B)

7. Square root is real only for nonnegative numbers.C)
Square root is real only for nonnegative numbers.

8. Theorem Vertical Line Test
A set of points in the xy - plane is the graph of a function if and only if a vertical line intersects the graph in at most one point.

9. y x
Not a function.

10. y x
Function.

11. Determine the domain, range, and intercepts of the following graph.y 4
(2, 3)
(10, 0)
(4, 0)
(1, 0) x
(0, -3) -4