Function Grapher, 1 and 2-Variable

Use +, -, *, / and ^ for addition, subtraction, multiplication, division, and power, respectively. However the use of * is optional for multiplication. That is,

can all be entered as written. But avoid using x2, for example, where a literal number comes right after an expression. Use parentheses (…) for grouping.

In addition to algebraic functions such as linear, quadratic and other polynomial and rational functions, you can use any of these predefined functions in your expressions, including power functions, logarithmic and exponential functions, trigonometric functions and their inverses, and hyperbolic functions and their inverses. You can also use mathematical constants such as the number represented by e (= 2.718…; Euler's number, natural Logarithm base) and π (=3.14…; by typing pi) in function expressions.

• For graphing a 1-variable function f(x) enter the function in the text box labelled "f(x) = " using x as the independent variable. You might need to select the radio button 2D(1-variable).
• When graphing a 2-variable function with the Function Grapher 3D select the radio button 3D(2-variable). The label of the function expression box changes to "f(x,y) = ". Enter the function using x and y as the independent variables.

After you have entered the function, press the Show Graph button. The Function Grapher will start the process of graphing. The graph of a one-variable function will appear as a curve instantly in most cases (if you have a fast computer), and if you are graphing a two-variable function with Function Grapher 3D the graph will be constructed as a surface by drawing a set of curves, namely, the x-direction and the y-direction contours.

When graphing a two-variable function with Function Grapher 3D, you can set the contours spacing by entering an integer in the corresponding text-box. The bigger the contours spacing, the more dispersed will the contours be and consequently the process of graphing will be faster.

If you want to graph more than one function with Function Grapher Applets press the Graph Multiple Functions button. A window will open. Input the number of functions (default 2 functions) you want to graph and enter each function in the enabled text boxes. Finally, press Graph All Functions button. If the function expressions are valid, all the graphs will be drawn on the applet. Otherwise, every function before the first with syntax error will be graphed, and an error message will identify that function and displays feedback.

By pressing the Snapshot button on the multiple functions input window the Function Grapher lets you view the graph of the individual functions. (if they can fit in the small area provided). This will also give you feedback whether you have made syntax error.

The expression

is entered as

or alternatively as

To evaluate the function at a particular x value enter that value in the text box provided and press the = button. You can enter any constant expression for the x values. For example, the expression

is a valid expression for the x value which can then be entered as

Similarly, when using Function Grapher 3D, to evaluate a two variable function at a particular point (x,y), input the x value and y value as constant expressions separated by comma in the text box provided.

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Predefined Functions and Constants for Function Grapher

Mathematical Constants Function Grapher 3D)

• pi for 3.14... .
• e for 2.718... .

Power and Absolute Value Functions

• Power Function x^r
• Square Root Functionsqrt(x) or x^.5
• Absolute Value Function abs(x)

Exponential and logarithmic Functions

• Exponential Function exp(x) or e^x
• Natural logarithm Function ln(x)
• Logarithm Function to the base 10 log(x)

Trigonometric Functions

• Sine Function sin(x)
• Cosine Function cos(x )
• Tangent Function tan(x)
• Cosecant Function csc(x)
• Secant Function sec(x)
• Cotangent Function cot(x)

Inverse Trigonometric Functions

• Arc Sine Function asin(x)
• Arc Cosine Function acos(x)
• Arc Tangent Function atan(x )
• Arc Cosecant Function acsc(x)
• Arc Secant Function asec(x)
• Arc Cotangent Function acot(x)

Hyperbolic Functions

• Hyperbolic Sine Function sinh(x)
• Hyperbolic Cosine Function cosh(x)
• Hyperbolic Tangent Function tanh(x)
• Hyperbolic Cosecant Function csch(x)
• Hyperbolic Secant Function sech(x)
• Hyperbolic Cotangent Function coth(x)

Inverse Hyperbolic Functions

• Inverse Hyperbolic Sine Function asinh(x)
• Inverse Hyperbolic Cosine Function acosh(x)
• Inverse Hyperbolic Tangent Function atanh(x)
• Inverse Hyperbolic Cosecant Function acsch(x)
• Inverse Hyperbolic Secant Function asech(x)
• Inverse Hyperbolic Cotangent Function acoth(x)

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