# Graphing Functions Calculator

An online graphing calculator to graph and determine the properties of function. This graphing calculator accepts most mathematical functions:

Trigonometric functions
sin(x) : sine function
cos(x) : cosine function
tan(x) : tangent function
cot(x) : cotangent function
sec(x) : secant function
csc(x) : cosecant function

Inverse Trigonometric Functions
arcsin(x) : inverse of sine function
arccos(x) : inverse of cosine function
arctan(x) : inverse of tangent function

logarithmic function base e
ln(x)
exponential function base e
exp(x)
absolute value function
abs(x)
and the special constants e and pi.

Buttons to zoom in and out the graph obtained are available and a trace to measure coordinates of points on the graphs of functions is also available. The coordinates of the trace are displayed on the top left corner of the screen.

Examples of expression for functions that may be entered.

sin(pi*x)-x^2

arctan(2*x-2)-2

exp(x^2-1)+ln(x)

How to use the calculator

1 - Press on the button "click here to start" to start the calculator (applet).

Your browser is completely ignoring the <APPLET> tag!

Interactive Tutorial

## 1 - x and y intercepts of graphs

Enter x^2-2*x-3 in the editing window (which means f(x) = x^2-2*x-3) of the graphing calculator. Determine (approximately) the x intercepts of the graphs (these are the points of intersection of the graph with the x axis). Determine the y intercept (this is the point of intersection of the graph with the y axis).

The x intercepts are found by solving x^2-2*x-3 = 0 and the y intercept is given by f(0). Solve the equation x^2-2*x-3 = 0 and find f(0) and compare to the x and y intercepts determined graphically.

## 2 - Even and odd functions

Enter x^2 + abs(x) in the editing window (which means f(x) = x^2 + abs(x) , abs means absolute value). Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests for even: f(x) = f(-x) and for odd: f(x) = - f(-x).

Enter x^3+1/x in the editing window (which means f(x) = x^3+1/x). Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests.

Enter x^3+abs(x) in the editing window (which means f(x) = x^3+abs(x)). Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests

## 3 - Determine Domain of a Function From Graph

Enter sqrt(4 - x^2) in the editing window (which means f(x) = sqrt(4 - x^2) , sqrt means square root). Verify graphically that the domain of f is given by the interval [-2 , 2].

Enter sqrt(-x + 1) in the editing window (which means f(x) = sqrt(-x + 1). Use the graph of f to determine its domain.

Enter 1 / (x^2 - 1) in the editing window (which means f(x) = 1 / (x^2 - 1)). Use the graph of f to determine its domain.

As an exercise find the domains of the above functions and compare with the domains found graphically above.

If needed,
Free graph paper is available.

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Updated: February 2015