Entering Functions

- The Basics
- Variables
- Arithmetic Operators
- Built-in Functions
- Turning Graphs On/Off
- Using X-Scan and Y-Scan
- Syntax Errors

The Basics:

Basically, the applet will display the graphs of up to four functions at once. You type a function in one of the input fields beneath the graphing area, and press the <Enter> or <Return> key on your keyboard. If you are used to entering functions in a graphing calculator, entering functions in the graphing applet should pose no problems for you.

Variables:

The applet recognizes only the variables "x" and "y". X is assumed to be the independent variable and is graphed on the horizontal axis, and y is assumed to be the dependent variable and is graphed on the vertical axis.

Arithmetic Operators:

The applet uses the standard arithmetic operators:

- "+" for addition
- "-" for subtraction
- "*" for multiplication. Implied multiplication is supported. In other words, you may type "3*x" or "3x" to mean "three times x".
- "/" for division
- "^" for exponentiation
- "()" - parentheses group symbols to indicate order of operations, as in standard algebra. The "normal" order of operations is observed in expressions - multiplications and divisions first, then additions and subtractions. This order can be changed using parentheses. That is, the expression " 2*3 + 4" evaluates to 10, while the expression "2*(3 + 4)" evaluates to 14.

Built-In Functions:

The applet supports several elementary functions, including:

- Algebraic/Arithmetic Functions
**:****abs(expression)**- returns the**absolute value**of its argument, which may be any real-valued expression.**int(expression)**- returns the**greatest integer**less than or equal to the value of the argument.**pi**- returns the constant**p.**(This function has no parentheses nor argument.)**rnd**- returns a**random number**in the range (0, 1)**rni(start expression, end expression)**- returns a**random integer**in the range [start expression, end expression]**sqr(expression)***or***sqrt(expression)**- returns the**square root**of its argument.

- Trigonometric Functions - arguments are in radians.
**cos(expression)**- returns the**cosine**of its argument.**cot(expression)**- returns the**cotangent**of its argument.**csc(expression)**- returns the**cosecant**of its argument.**sec(expression)**- returns the**secant**of its argument.**sin(expression)**- returns the**sine**of its argument.**tan(expression)**- returns the**tangent**of its argument.

- Exponential & Logarithmic Functions
**exp(expression)**- returns the value**e**, where "e" is the base of the natural logarithms, and the argument can be any real-valued expression.^{expression}**ln(expression)**- returns the value of the**natural logarithm**function.**log(base, expression)**- returns the**logarithm****(log**of the expression to the given base._{base}expression)

- Inverse Trigonometric Functions
**aco(expression)***or***acos(expression)**- returns the**arccosine**(inverse cosine) of its argument.**acot(expression)**returns the**arccotangent**(inverse cotangent) of its argument.**acsc(expression)**returns the**arccosecant**(inverse cosecant) of its argument.**asec(expression)**returns the**arcsecant**(inverse secant) of its argument.**asi(expression)***or***asin(expression)**- returns the**arcsine**(inverse sine) of its argument.**atan(expression)**- returns the**arctangent**(inverse tangent) of its argument.

- Hyperbolic Functions
**cosh(expression)**- returns the**hyperbolic cosine**of its argument.**coth(expression)**- returns the**hyperbolic cotangent**of its argument.**csch(expression)**- returns the**hyperbolic cosecant**of its argument.**sech(expression)**- returns the**hyperbolic secant**of its argument**sinh(expression)**- returns the**hyperbolic sine**of its argument.**tanh(expression)**- returns the**hyperbolic tangent**of its argument.

- Inverse Hyperbolic Functions
**icoh(expression)**- returns the**inverse hyperbolic cosine (cosh**of its argument.^{-1})**icth(expression)**- returns the**inverse hyperbolic cotangent****(coth**of its argument.^{-1})**icsh(expression)**- returns the**inverse hyperbolic cosecant****(csch**of its argument.^{-1})**iseh(expression)**- returns the**inverse hyperbolic secant****(sech**of its argument^{-1})**isih(expression)**- returns the**inverse hyperbolic sine (sinh**of its argument.^{-1})**itah(expression)**- returns the**inverse hyperbolic tangent (tanh**of its argument.^{-1})

Turning Graphs On/Off:

You can use the checkbox to the left of the function to turn the
graph of particular functions on and off. ** **

X-Scan & Y-Scan

If X-Scan is checked, the program will sketch curves that are
more-or-less vertical pretty well, but will tend to skip a lot of
points across lines that are more-or-less horizontal (See "How
It Works"). Y-Scan will draw the more-or-less horizontal parts of
a curve pretty well, but not the more-or-less vertical parts. You may
want to get the viewing rectangle you
want, then check both X-Scan and Y-Scan to get the best graph.**
**

This feature has no effect on the graph of an explicit (y = f(x)) function.

If you make a mistake typing your function, the program will ignore the input and display a "syntax error" message in the message area to the right of the graph display. At the moment, this message is not very helpful in identifying your error - I'm working on that.

last update April 14, 2008 by JL Stanbrough