Copyright © Cengage Learning. All rights reserved. Functions Copyright © Cengage Learning. All rights reserved.

Copyright © Cengage Learning. All rights reserved. 2.1 What is a Function? Copyright © Cengage Learning. All rights reserved.

Objectives Evaluating a Function

Evaluating a Function

Evaluating a Function In the definition of a function the independent variable x plays the role of a placeholder. For example, the function f (x) = 3x2 + x – 5 can be thought of as To evaluate f at a number, we substitute the number for the placeholder.

Example 2 – Evaluating a Function Let f (x) = 3x2 + x – 5. Evaluate each function value. (a) f (–2) (b) f (0) (c) f (4) (d) f ( x+h ) Solution : To evaluate f at a number, we substitute the number for x in the definition of f. (a) f(–2) = 3  (–2)2 + (–2) – 5 = 5

Example 2 – Solution (b) f (0) = 3  02 + 0 – 5 = –5 cont’d (b) f (0) = 3  02 + 0 – 5 = –5 (c) f (4) = 3  (4)2 + 4 – 5 = 47 (d) f (x+h) = 3(x+h)2 + x+h – 5 = 3x2 + 6xh + 3h2 + x + h – 5