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Functions
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2. Copyright © Cengage Learning. All rights reserved.
2.1
What is a Function?
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3. Objectives
Evaluating a Function

4. Evaluating a Function

5. 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.

6. 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

7. Example 2 – Solution (b) f (0) = 3  02 + 0 – 5 = –5
cont’d
(b) f (0) = 3  – 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