Precalculus Functions and Graphs
Basic Definitions and Notations Concepts 1

|  |  | Definition |  |
. |
A function is a correspondence (or rule) that assigns to each member of some set called the domain exactly one member of a set called the range .

To describe function arrows can be used.

This correspondence is a function. | This correspondence is not a function.

When a function is given by the formula or equation, function values are found by substituting into the formula. That is true even if the inputs are not specific numbers.

Example 1. f(x) = 2 · x - 5; find f(-3).

Solution

f(-3) | = | 2 · (-3) - 5 Substituting the input, -3
| = | -6 -5
| = | -11.

Example 2. f(x) = 2 · x - 5; find f(5· x).

Solution

f(5 · x) | = | 2 · (5 · x) - 5 Substituting the input, 5 · x
| = | 10 · x - 5.

Example 3. f(x) = x2 - 3; find f(1- 2 · x ).

Solution

f(1 - 2 · x) | = | (1 - 2 · x)2 - 3 | Substituting the input, 1 - 2 · x
| = | 1 - 4 · x + 4 · x2 - 3 | Squaring 1 - 2 · x
| = | 4 · x2 - 4 · x - 2. | Simplifying

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