Download presentation

Presentation is loading. Please wait.

Published byDillon Tillie Modified over 4 years ago

1
**Relations, Functions and Evaluations By Mr. Porter.**

2
**Relations and Functions.**

Definitions: Relations: A relation is a set of ordered pairs (points), and is usually defined by some property or rule. The Domain of a relation is the set of all first elements of the ordered pairs. The Range of a relation is the set of all second elements of the ordered pairs. A point (x,y) is a relation, with the first element x being the domain and the second element y being the range of the point. Example of a RELATIONS Dave Sally Joe John 30 25 22 Ordered Pairs (Dave, 30) (Sally, 25) (Joe, 22) (John, 30) (Dave, 22) Domain Range

3
**Definitions Functions:**

A function is a set of ordered pair in which no two ordered pairs have the same x-coordinate or first value. The domain of a function is the set of all x-coordinates of the ordered pair. The range of a function is the set of all y-coordinates of the order pair. Vertical line Test: A relation is a function if and only if there is no vertical line that crosses the graph - curve more than once. Examples using vertical line test for a function. Every Vertical Line cuts the curve once.Therefore, this curve represents a FUNCTION. Every Vertical Line cuts the curve once.Therefore, this curve represents a FUNCTION. A Vertical Line cuts the curve two or more times.Therefore, this curve represents a RELATION.

4
Exercise 1 Which of the following curves would represent a function or a relation. a) b) c) d) Relation Function Function Function e) f) g) h) Relation Relation Function Function i) Function

5
Function Evaluation Notation used to represent a function is of the form f(x), g(x), h(x), p(x) ……, or upper-case F(x), H(x), G(x), … Evaluating a function is the process of replacing the variable with a number or another expression, then either evaluating the result numerically or simplifying the resulting express by expanding. Examples 1) If f(x) = x2 - 3x, evaluate: a) f(5) b) f(-2) c) f(a+3) This means that x = (a+3) This means that x = 5 f(x) = x2 - 3x f(x) = x2 - 3x f(x) = x2 - 3x f(5) = (5)2 - 3(5) f(-2) = (-2)2 - 3(-2) f(a+3) = (a+3)2 - 3(a+3) Expand brackets f(5) = 10 f(-2) = 10 f(a+3) = a2 + 6a a - 9 Simplify = a2 + 3a It is a good idea to place the value in (..)

6
**Exercise: Evaluate the following functions.**

1) Given f(x) = 4 – x3 a) find f(2). b) find f(-3). 2) Given g(x) = 5x – x2 a) find g(1). b) find g(-4). 3) Given h(x) = a) find h(1). (exact value) b) find h(-4). (exact value) a) f(2) = -4 a) g(1) = 4 b) f(-3) = 31 b) g(-4) = -36 4) Given f(x) = 3x - 5 a) f(2a) b) f(a - 3) 5) Given h(x) = 2x - x2 a) h(2 - x) b) h(x2-1) a) f(2a) = 6a – 5 a) h(2 - x) = 2x - x2 b) f(a - 3) = 3a – 14 b) h(x2-1) = -x4 + 4x2 - 3

7
Multi-Functions These function have a domain [ x-value] restriction which select the expression to be used. Example In this case x = 3, we select the expression x2+2 to evaluate Use f(x) = To evaluate a) f(2) b) f(-5) c) f(1) + f(3) + f(-2) x2 + 2 for x > 2 3 – x for 0 ≤ x ≤ 2 | x | for x < 0 In this case x = 1, we select the expression 3 – x to evaluate In this case x = -2, we select the expression | x | to evaluate In this case x = 2, we select the expression 3 – x to evaluate In this case x = -5, we select the expression | x | to evaluate f(2) = 3 – (2) = 1 f(-5) = | -5 | = 5 f(1) + f(3) + f(-2) = (3 - 1)+ (32+2) + | -2 | = = 15

8
Exercise 1) Use f(x) = To evaluate a) f(2) b) f(1) + f(3) + f(-2) x2 for x > 2 3x for 0 ≤ x ≤ 2 5 for x < 0 2) Use g(x) = To evaluate a) g(2) b) g(1) + g(3) – g(-4) x2 + 3 for x > 0 | 3 + x | for x ≤ 0 a) f(2) = 6 b) f(1) + f(3) + f(-2) = 17 a) g(2) = 7 b) g(1) + g(3) – g(-4) = 15

Similar presentations

Presentation is loading. Please wait....

OK

AP Calculus Notes Section 1.2 9/5/07.

AP Calculus Notes Section 1.2 9/5/07.

© 2018 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