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 ## Trigonometric functionssin(x) : sine functioncos(x) : cosine function tan(x) : tangent function cot(x) : cotangent function sec(x) : secant function csc(x) : cosecant function ## Inverse Trigonometric Functionsasin(x) : inverse of sine functionacos(x) : inverse of cosine function atan(x) : inverse of tangent function ## Hyperbolic Functionssinh(x) : hyperbolic sine functioncosh(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 Functionslog(x,a) , logarithmic function base to the base alog(x) , logarithmic function to the base e ## Exponential Functionsa^x , exponential function to the base ae^x , exponential function to the base a ## and Square Root Functions Absolute Value and Square Root Functionsabs(x) , absolute value functionssqrt(x) , square root function ## Special ConstantsSpecial 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.
## Interactive Tutorial## 1 - x and y intercepts of graphs- 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).
- 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- 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).
- 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 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.
- 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 and Range 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]. Verify graphically the range is [0 , 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.
- Enter -2sin(x) in the editing window (which means f(x) = -2sin(x)). Use the graph of f to determine its domain and range.
- 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.
- 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.
- As an exercise find the domains of the above functions and compare with the domains found graphically above.
Free graph paper available.
## More References and LinksProperties of Trigonometric FunctionsInverse 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. |