Alegebra 2A Function Lesson 1 Objective: Relations, and Functions

1. Relation A set of ordered pairs (x, y). Examples: (7, 2), (0, -5), (-2.4, -18),… 2. Domain – The first coordinate (x) of a relation. (Independent Variable) 3. Range – The second coordinate (y) of a relation. (Dependent Variable)

Examples: 4. Function – A relation in which each element in the domain (x) corresponds to one, and only one, element in the range (y). Examples: State the domain and range of each relation. Also determine if it is a function. Ex1

(a) (8, 5), (7, -2), (-2, 9), (0, 3) (b) (-3, 4), (14, 0), (6, 4), (2, 8) (c) (1, 6), (1, -7), (0, 0), (5, 13) d)

One-To-One Correspondence A situation in which each domain value (x) corresponds to exactly one element in the range (y), and vice versa. Example: (7, 9), (-1, 15), (2, 0), (8, -3)

Based on each graph below, which represents a function? Ex2 b. c. d.

Vertical Line Test If any vertical line intersects a graph in more than one point, then the graph is not a function.

Ex. 3 For the graph of f(x) below: Find the output for the input value 4. Find the inputs whose output value is 0. Find f(1) If f(x) = -2, then x = ? Find f(-2) State the domain and range of f(x). Is f(x) a function? A 1–1 function? Ex. 3

For g(x) = x2 + 7x – 2, find: a) b) c) d) e) f) Ex. 4

Ex. 5

Ex. 6 Graph the functions f(x) = 2x and g(x) = 2x + 4 on the same axis. What do you notice? Why is this so?

Ex. 7 Use the graph of each function to Identify its domain and range. a)

b)

c)

d)

Function Lesson 1 Assignment Numbers (1 – 14)