# Graphing Functions Calculator

An online graphing calculator to graph and determine the properties of functions. This graphing calculator accepts most mathematical functions and a list is given below.

## How to Use Graphing Functions Calculator

1 - Enter the expression defining function f(x) that you wish to plot and press on the button "Plot f(x)". The variable in the expression of the function is the small letter x.

f(x) =

Hover the mousse cursor over the graph to trace the coordinates.
Hover the mousse cursor on the top right of the graph to have the option of download the graph as a png file.

All the functions listed below are accepted by this calculator and they may be copied and pasted on the "f(x)" input window above if needed.

## 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

asin(x) : inverse of sine function
acos(x) : inverse of cosine function
atan(x) : inverse of tangent function

## Hyperbolic Functions

sinh(x) : hyperbolic sine function
cosh(x) : hyperbolic cosine function
tanh(x) : hyperbolic tangent function
coth(x) : hyperbolic cotangent function
sech(x) : hyperbolic secant function
csch(x) : hyperbolic cosecant function

## Logarithmic Functions

log(x,a) , logarithmic function base to the base a
log(x) , logarithmic function to the base e

## Exponential Functions

a^x , exponential function to the base a
e^x , exponential function to the base a

## and Square Root Functions Absolute Value and Square Root Functions

abs(x) , absolute value functions
sqrt(x) , square root function

## Special Constants

Special constants e and pi are used as they are, leaving a space any of the constants and another constant or variable.
Example: sin(pi x) ; e^x , ...
You may hover the mousse cursor to read coordinates of any point on the graph. Zoooming is also available at the top right hand side of the graph and you may also download png files with the graph in it.

Examples of expression for functions that may be entered.
sin(pi*x)-x^2
atan(2*x-2)-2
exp(x^2-1)+log(x,3)

## Interactive Tutorial

### 1 - x and y intercepts of graphs

1. Enter function 2 x - 4 in editing "f(x)" window (which means f(x) = 2 x - 4) of the graphing calculator above and find the x and y intercepts graphically and check the answer by calculation. x - intercept is the solution to f(x) = 0 and the y-interecept is given by f(0).
2. Enter x^2-2 x - 3 in the editing "f(x)" window (which means f(x) = x^2 - 2 x - 3) of the graphing calculator above. 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

1. Enter abs(x) in the editing window (which means f(x) = 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).
2. 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).
3. Enter x^3 in the editing window (which means f(x) = x^3). Use the graph of f to determine whether f is even, odd or neither? Confirm your answer using analytical tests.
4. 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.
5. 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 and Range of a Function From Graph

1. 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]. Verify graphically the range is [0 , 2].
2. Enter sqrt(x^2-9) in the editing window (which means f(x) = sqrt(x^2 - 9) , sqrt means square root). Use the graph of f to determine its domain and range.
3. Enter -2sin(x) in the editing window (which means f(x) = -2sin(x)). Use the graph of f to determine its domain and range.
4. Enter sqrt(-x + 1) in the editing window (which means f(x) = sqrt(-x + 1). Use the graph of f to determine its domain and range.
5. 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 and range.
6. As an exercise find the domains of the above functions and compare with the domains found graphically above.

Free graph paper available.

Properties of Trigonometric Functions
Inverse Trigonometric Functions
Graphs of Hyperbolic Functions
Logarithmic Functions
Exponential Functions
Absolute Value Functions
Square Root Functions
How to Find x and y Intercepts Of Graphs?
How to Find x and y Intercepts Of Graphs?
Even and Odd Functions
Even and Odd Functions
Domain and Range of a Function
Graphing Calculators.