Download presentation

1
Functions and Relations

2
Relations Functions Definition: Definition: A relation is a set of ordered pairs. A function is a relation such that for each x, there is exactly one corresponding y. Examples: {(1, –1), (2, 1), (3, 3), (4, 5)} 2. {(–2, 3), (–1, 1), (1, –1), (3, 1), (4, 3)} 3. {(–3, 1), (–1, 3), (–1, –1), (1, 4), (1, –2)} 4. {(–2, 2), (–2, –1), (4, 2), (4, –1)} is a function. a function. not a function. not a function. Definitions: Domain is the set of all possible values of x of a function (or a relation). Range is the set of all possible values of __ of a function (or a relation). y What are the domain and range of the four examples above? 1. Domain = {1, 2, 3, 4} Range = {–1, 1, 3, 5} 2. Domain = { } Range = { } 3. Domain = { } Range = { } 4. Domain = { } Range = { } –2, –1, 1, 3, 4 3, 1, –1 –3, –1, 1 1, 3, –1, 4, –2 –2, 4 2, –1

3
**The graph of a relation is a function if and only if**

{(1, –1), (2, 1), (3, 3), (4, 5)} {(–2, 3), (–1, 1), (1, –1), (3, 1), (4, 3)} {(–3, 1), (–1, 3), (–1, –1), (1, 4), (1, –2)} {(–2, 2), (–2, –1), (4, 2), (4, –1)} y x O 2 4 6 –6 –4 –2 y x O 2 4 6 –6 –4 –2 y x O 2 4 6 –6 –4 –2 y x O 2 4 6 –6 –4 –2 Function Function Not a Function Not a Function y x O 2 4 6 –6 –4 –2 y x O 2 4 6 –6 –4 –2 y x O 2 4 6 –6 –4 –2 y x O 2 4 6 –6 –4 –2 The Vertical Line Test: The graph of a relation is a function if and only if every vertical line drawn only intersects the curve in at most one point.

4
**X Y X Y Function Notation Ex. 1: {(1, 2), (2, 4), (3, 6), (4, 8)}**

1 2 3 4 9 x f: 2x x f: x2 2x x f x2 x f Note: f(x) is read as “f of x”, and it doesn’t mean f times x; if it does, the notation would have been fx. But the most conventional way to denote a function (Ex. 2) is: f(x) = x2 Name of the function Name of the variable (i.e., the input) Definition of the function; here, the definition is: no matter what the input is, the output will be the square of the input. Function-Value Evaluation Ex. 1: f(x) = x2 + 1 a) f(2) = = 5 b) f(5) = = 26 c) f(abc) = (abc)2 + 1 = a2b2c2 + 1 Ex. 2: g(t) = t2 – 2t + 3 a) g(–3) = (–3)2 – 2(–3) + 3 = 18 b) g(2n) = (2n)2 – 2(2n) + 3 = 4n2 – 4n + 3 Ex. 3: H(z) = 2z2 – 5 a) H(4) = 2(4)2 – 5 = 27 b) H(z + 1) = 2(z +1)2 – 5 = 2(z2 + 2z + 1) – = 2z2 + 4z – 3

Similar presentations

OK

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1.2 Basics of Functions and Their Graphs.

Chapter 1 Functions and Graphs Copyright © 2014, 2010, 2007 Pearson Education, Inc. 1 1.2 Basics of Functions and Their Graphs.

© 2019 SlidePlayer.com Inc.

All rights reserved.

To make this website work, we log user data and share it with processors. To use this website, you must agree to our Privacy Policy, including cookie policy.

Ads by Google