Theory of Functions and Graphs

Functions and Their Graphs:

Chapter Summary:

The 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 = -2x2 -7x + 2
Cubic               The highest power over the x variable(s) is 3      y = x3 + 3x2 + x
Logarithmic     The log of the x variable is taken                          y = log (x)

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