1. Domain and Range From a Graph

2. Every input has only one output
Every input has only one output. Use the vertical line test to determine if a graph represents a function.
The set of all possible x values. How far left and right does the graph go?
The set of all possible y values. How far down and how far up does the graph go?
Function:
Domain:
Range:

3. Interval Notation
*Intervals are noted with brackets [ ] parenthesis ( ) or a combination of both. *A bracket means a value _________. It is the same as a __________ for an inequality. *A parenthesis means a value______________ It is the same as an _________ for an inequality. *Infinity is ________________
IS included
closed circle
is NOT included.
open circle
always a parenthesis!

4. Practicing Interval Notation
1. -4 < x ≤ 5 2. x > 6 3. x ≤ 8
[ 3, 12)
5. (- ∞, -1)
6. [ -7, ∞ )
(-4, 5 ]
3 ≤ x < 12
Can’t have one infinity
- ∞ < x < -1 6
(6, ∞)
x < -1
Can’t have one infinity
-7 ≤ x < ∞ 8
(-∞, 8 ]
x ≥ -7

5. Ex #1: Finding the Domain
First, how far LEFT does the graph go?
Next, how far right does the graph go?
Up to, but not including -5
Up to and including 4
1. Interval Notation:
2. Inequality:
-5 < x ≤ 4
3. Set Notation:
{x -5 < x ≤ 4}
(-5,
4 ]

6. Ex #1: Finding the Range First, how far DOWN does the graph go?
Next, how far UP does the graph go?
Down to and including -2
Up to and including 3
1. Interval Notation:
2. Inequality:
-2 ≤ y ≤ 3
3. Set Notation:
{y -2 ≤ y ≤ 3}
[-2,
3 ]

7. Ex #2: Finding the Domain
First, how far LEFT does the graph go?
Next, how far right does the graph go?
It never ends, so ∞
It never ends, so - ∞
1. Interval Notation:
2. Inequality:
- ∞ < x < ∞
3. Set Notation:
{x - ∞ < x < ∞}
(- ∞,
∞ )

8. Ex #2: Finding the Range First, how far DOWN does the graph go?
Next, how far UP does the graph go?
Down to and including -3
It never ends, so ∞
1. Interval Notation:
2. Inequality:
y ≥ -3
3. Set Notation:
{y y ≥ -3}
[- 3,
∞ )

9. What is the domain of this function?
A 0 ≤ x ≤ 9
B ≤ x ≤ 9
C 0 ≤ x ≤ 5
D -1 ≤ x ≤ 5 ✔

10. ✔ What is the range of this function? A 0 < y < 100
B 0 ≤ y ≤ 100
C 0 ≤ y ≤ 5
D 0 < y < 5 ✔

11. What is the domain of the function?
A -4 < x ≤ 2
B -4 ≤ x < 2
C -2 < x ≤ 6
D -2 ≤ x < 6 ✔