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## Theory of Functions and Graphs

Functions and Their Graphs::Chapter SummaryThe graph of a function can provide us a great deal of information regarding the function. In this section we will use the graph of a function to calculate the function, determine the x- and y -intercepts (if any one), the domain and range, and find out where the function is decreasing or increasing (that is, a significant idea in calculus).

To state that f (−3) = 1 signifies that the point (−3, 1) is on the graph of f (x). When (5, 4) is a point on graph of f (x), then f (5) = 4.

Key topics included in this chapter:1) Graphs and Graphing Utilities

2) Lines in the Plane

3) Functions

4) Graphs of Functions

5) Shifting, Reflecting, and Stretching Graphs

6) Combinations of Functions

7) Inverse Functions

The table given below briefly defines some of the function:

Function Definition Example

Linear The highest power over the x variable is y = 2x + 1

Quadratic The highest power over the x variable(s) is 2 y = -2x

^{2}-7x + 2Cubic The highest power over the x variable(s) is 3 y = x

^{3}+ 3x^{2}+ xLogarithmic The log of the x variable is taken y = log (x)

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