1. 4-1 FUNCTIONS
Objectives:
1. Identify a function
2. Find domain, range, and zeros of a function.

2. IDENTIFYING FUNCTIONS
A function is a rule that assigns every
input element in the domain to exactly
one output element in the range.
Use the Vertical Line Test to decide if
a graph is a function.

3. DOMAIN: FROM EQUATIONS
The domain includes real number
inputs for which the function produces
real number outputs.
Look for:
 Denominators – can’t divide by 0
 Even roots – can’t be negative inside
Otherwise, domain is “all real numbers”

4. INTERVAL NOTATION
When using interval notation, the
symbol:
 ( means "not included" or "open".
 [ means "included" or "closed".
Example:
 as an inequality: 2 ≤ x < 6
 in interval notation: [2, 6)

5. NON-ENDING INTERVALS
Infinity is always expressed as being
"open" (not included).
Examples:
 ( 1 , ∞) means x > 1
 (- ∞, 6] means x ≤ 6
 (- ∞, 9) U (9, ∞) means x < 9 or x > 9
-or- all real #s except 9
U is the “union” symbol

6. EXAMPLE 1
Give the domain of each function.

7. YOU TRY!
Give the domain:

8. ANALYZING GRAPHS
Domain – set of x-coordinates of
points on the graph
Range – set of y-coordinates of
points on the graph
Zeros – x-intercepts

9. EXAMPLE 2
Find the domain, range and zeros:

10. YOU TRY!
Find the domain, range, and zeros: