Graphing Functions

To represent a function graphically, calculate the points or intervals in the function where it changes its behavior. To do so, find the following mathematical characteristics:

1.   Domain of the function.

2.   Intersections with the x-axis and y-axis.

3.   Asymptotes.

4.   Increases and decreases.

5.   Maxima and minima.

6.   Concavity and convexity.

7.   Inflection points.


Representation of a Function Example

Function

Domain

Domain of a Function

x-intercepts

x-intercepts

y-intercept

y-intercept

Asymptotes

Horizontal asymptote

Horizontal Asymptote

There are no vertical or oblique asymptotes.

Increases and Decreases

Increases and Decrease

Increases and Decrease

Increasing

Decreasing

Minimum

Minimum

Maximum

Maximum

Concavity and Convexity

Concavity and Convexity

Concavity and Convexity

Convexity

Concavity

Inflection Points

Inflection Points

Graph the Function

Graph the Function