Domain and Range From a Graph

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:

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!

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

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 ]

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 ]

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 < ∞} (- ∞, ∞ )

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, ∞ )

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

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

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