Entering Functions

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 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 eexpression, where "e" is the base of the natural logarithms, and the argument can be any real-valued expression.
• ln(expression) - returns the value of the natural logarithm function.
• log(base, expression) - returns the logarithm (logbaseexpression) of the expression to the given base.
• 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-1) of its argument.
• icth(expression) - returns the inverse hyperbolic cotangent (coth-1) of its argument.
• icsh(expression) - returns the inverse hyperbolic cosecant (csch-1) of its argument.
• iseh(expression) - returns the inverse hyperbolic secant (sech-1) of its argument
• isih(expression) - returns the inverse hyperbolic sine (sinh-1) of its argument.
• itah(expression) - returns the inverse hyperbolic tangent (tanh-1) of its argument.

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.

Syntax Errors:

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