# Functions and graphing functions

Draw the line How to plot a nice graph with sweaty shaky hands I have to make a terrible confession. My hands are sweaty and they shake a lot. I am generally a messy person and my wife complains that my desk is a nightmare. Due to the nature of the mathematics on this site it is best views in landscape mode. If your device is not in landscape mode many of the equations will run off the side of your device should be able to scroll to see them and some of the menu items will be cut off due to the narrow screen width.

Graphing In this section we need to review some of the basic ideas in graphing. We will only be reviewing some of the basic ideas. We will start off with the Rectangular or Cartesian coordinate system.

This is just the standard axis system that we use when sketching our graphs. Here is the Cartesian coordinate system with a few points plotted. Note as well that the order of the coordinates is important. We now need to discuss graphing an equation.

Section Graphing. In this section we need to review some of the basic ideas in graphing. It is assumed that you’ve seen some graphing to this point and so . Determining the nature of the function you are graphing. Jump to: Linear (straight lines), Quadratic (parabolas), Absolute value Remember that the high school curriculum is designed so that even relatively stupid students can get decent grades, provided that they . Notice that the graph in this example is the same shape as except that it has been moved down 4 units.; Graph y = -|x|; In creating the table of values, be careful of your order of operations. You should find the absolute value of x first and then change the sign of that answer.

The first question that we should ask is what exactly is a graph of an equation? A graph is the set of all the ordered pairs whose coordinates satisfy the equation. How do we tell this? All we need to do is take the coordinates of the point and plug them into the equation to see if they satisfy the equation.

Now, how do we sketch the graph of an equation? Of course, the answer to this depends on just how much you know about the equation to start off with. There are also many other kinds of equations that we can usually get the graph from the equation without a lot of work.

We will see many of these in the next chapter. In these cases we will need to recall that the graph is simply all the points that satisfy the equation. So, all we can do is plot points. Unfortunately, the answer there is we guess.

We pick some values and see what we get for a graph. If not we pick some more. Hopefully, by the end of this course you will have gained some of this knowledge.

## How to Graph Piecewise Functions (5 Powerful Examples!)

Show Solution Now, this is a parabola and after the next chapter you will be able to quickly graph this without much effort. Here is a table of values for this equation.Let's do a couple more examples graphing rational functions. So let's say I have y is equal to 2x over x plus 1. So the first thing we might want to do is identify our horizontal asymptotes, if there are any. Function worksheets in this page contain finding domain and range from the list of ordered pairs and graph; function tables; plotting points and graphing function; composition of two or more functions.

Moreover, we can see how Piecewise Functions can help us to establish rules for common step functions, such as the Greatest Integer Function. The trick in graphing the Greatest Integer Function is to first understand that it looks like steps or a staircase, and that we are actually rounding down to the integer less than or equal to the value we plug in.

This Precalculus review (Calculus preview) lesson explains how to put all the pieces (intercepts and asymptotes) together to graph rational functions. Determining the nature of the function you are graphing. Jump to: Linear (straight lines), Quadratic (parabolas), Absolute value Remember that the high school curriculum is designed so that even relatively stupid students can get decent grades, provided that they .

In this section we discuss graphing functions including several examples of graphing piecewise functions.

Function Grapher and Calculator