Function grapher - Math Open Reference

Function Explorer

Operating instructions

This is a free web-based function graphing tool that allows you to plot up to three functions on the same set of axes. In the functions you can refer to up to three independent variables that are controlled by sliders. This allows you to easily see the effect of changes since the graphs change in real time as you drag the sliders.

Enter a formula into one of the three input boxes ( f(x), g(x), or h(x) ), then press GRAPH or the keyboard Enter key. For example:

Press Clear, then in the top function box (f(x)) enter "cos(x)" then press GRAPH or the Enter key on the keyboard. The function will be plotted in the window above.

The syntax rules are the same as for the typed-in expressions for the Math/Scientific Calculator.

Arithmetic Operators

Function	Typed in
Add	+
Subtract	-
Multiply	*
Divide	/
Exponent	^

Built-in functions

The grapher has the following built-in functions. The function names are not case sensitive. Example: sin(x) is the same as Sin(x)

Function Example Description

Sine sin(12) The trigonometry sine function.

Cosine cos(12) The trigonometry cosine function.

Tangent tan(12) The trigonometry tangent function.

Arc Sine asin(x) The trigonometry inverse sine function. The angle whose sine is x.

Arc Cosine acos(x) The trigonometry inverse cosine function. The angle whose cosine is x.

Arc Tangent atan(x) The trigonometry inverse tangent function. The angle whose tangent is x.

Logarithm log(x) The log left 10 of x. The power to which you must raise the 10 to get x.

Natural Log ln(x) The log base e of x. The power to which you must raise e to get x.

Exp exp(x) e (approx 2.718) raised to the power of x.

Min min(a,b) Returns a or b whichever is smallest.

Max max(a,b) Returns a or b whichever is largest.

Abs abs(x) Returns the absolute value of x (always positive)

Pow pow(x,y) Returns x raised to the power y. pow(2,3) = 8

Round round(x) Returns x rounded off to the nearest whole number

floor floor(x) Returns the highest integer less than or equal to x

ceil floor(x) Returns the smallest integer greater than or equal to x

Constants

There are two constants you can refer to. They are not case sensitive.

Pi - approximately 3.142.. See PI definition for more.
e - approximately 2.718..

For example you could enter sin(pi) or e^2.1

Scientific notation

Scientific notation (E.G. 1e+3 for 1000) is not supported.

Automatic multiplication

If a function (such as sin() ) is preceded by a number, the grapher assumes you want to multiply them. For example 3cos(2.1) will be automatically treated as if you entered 3*cos(2.1): three times the cosine of 2.1

Note: This feature can mislead you. For example if you enter 1/2sin(.5) the grapher inserts a multiply between the 2 and the sin. Since there are no parentheses,it is executed from left to right so it operates as though you meant one half of sin(.5).

Automatic parenthesis balancing

When you press GRAPH or enter, it will automatically add enough closing parentheses to balance them. For example, if you enter 2+(sin(x it will add two extra closing parentheses so they balance and evaluate it as 2+sin(x)) Note: This may not always produce the desired result. It is best to always enter the correct expression yourself.

Using the cursor

If you click on "show cursor" a thin vertical line appears. If you drag this line with the mouse, it shows the values of each function where the cursor intersects that function.

Changing axis limits

At each end of the x and y axis is a box containing the end values. To change them, simply edit them in place and press GRAPH or the Enter key again.

The grapher will check to ensure that the lower value is at the bottom of the y axis or the left of the x-axis. Negative number are allowed.

Using variables

When you enter your equations, you can refer to up to three variables that are controlled by sliders. These are named a,b and c, and you can adjust the value of each variable by moving the slider up or down. You can also enter an exact value into the box at the top of the slider, followed by the GRAPH button or the Enter key.

For example, in the chart above, press 'reset'. Note that the first function is sin(a*x). This means that each time a point is plotted, it is the sine of the current value of x times the variable a. This variable is controlled by the slider on the right, so as you move the slider you can see the effect of varying its value.

You can change the range of the slider by clicking on "range" below it. A dialog will appear that allows you to set the range of each slider separately.

You can control how many sliders you want to see with the pull-down list above them. You can still refer to the values even if they are hidden.

Full screen view

Click on "full size" under the grapher. A new window will open with a new grapher in it that is as large as your monitor will allow. This can be useful in a classroom with a projector.

Note: In some browsers (notably Safari), this will be ignored if the browser is set to block popups. (This blocking should not strictly happen, since the pages come from the same domain, but some browsers block it anyway).

Graph anomalies?

Under some conditions, a graph may seem to have errors. To learn more about this see Graphing tool limitations.

Acknowledgments

The function parser in this applet was developed by Douglas Ensley and Barbara Kaskosz.

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