1. PreCalculus 1st Semester
1.2 Functions
PreCalculus
1st Semester

2. Objectives:
To decide whether relations between variables represent a function.
To use function notation and evaluate functions.
To find the domain of functions.

3. Relation: A group of ordered pairs.
Pairs of quantities that are related to each other by some rule of correspondence.
For example: (person, grade)
(hours worked, dollars made)
(radius, area of a circle)

4. Function:
A relation that matches each item from one set with exactly one item from a different set.
(each x pairs with exactly one y)
For example:
(1,2)(3,4)(5,6) - function
(1,2)(1,3)(4,5) - not a function

5. Domain and Range
Domain: set of inputs or independent values (x values)
Range: set of outputs or dependent values (y values)

6. Example 1: Testing for Functions
Decide whether the relation represents y as a function of x.
(a)
(b)
Input x 2 3 4 5
Output y 11 10 8 1
Table: Not a function
Graph: Function

7. Example 2: Which of the equations represent(s) y as a function of x?
(a) (b)

8. Function Notation
As long as an equation is a function, it can be written using function notation.
For example:
Other letters may also be used:

9. Example 3:

10. Piecewise Function:
A piecewise function is a function that is defined by two or more equations over a specified domain.

11. Example 4:
Evaluate the function when x = -1 and 0.

12. Implied Domain:
The set of all real numbers for which the function is defined.
For example:
Domain: All real numbers except 2 and -2

13. How to find restrictions on domain:
Denominator with variables
Set denominator = 0 and solve for variable
Radicals (even root) with variables
Set radicand or 0 and solve
(radicals in the numerator cannot be imaginary)
(radicals in the denominator cannot be zero or imaginary)

14. Example 5:
Find the domain of each function: