An online graphing calculator to draw the graph (in red) fomed by reversing the ordered pairs corresponding to all points on the graph (blue) of a function f that you input. If function f is a one to one function, the graph obtained is that of the inverse of f. If needed, Free graph paper is available.
How to use the calculator
1 - Press the button "click here to start" to start the calculator (applet).
2 - Enter a formula for function f (x^2 for example) and press "enter". Two graphs are displayed: the graph of function f (in blue) that you input, a parabola, and the graph (in red) of the reversed ordered pairs.
Interactive Tutorial
1 - Enter sqrt(x) in the editing window of the calculator, which means f(x) = sqrt(x), and press enter. sqrt stands for square root. Is the graph of the reversed pairs (in red) that of a function? If it is the graph of a function, it is the inverse function of f(x) = sqrt(x). Find, analytically, the inverse function of f(x) = sqrt(x) and compare it to the graph obtained.
2 - Enter x^2 in the editing window, which means f(x) = x^2, and press enter. Is the graph of of the reversed pairs (in red) that of a function? If it is not a function, is f a one to one function?
3 - Enter x^3 in the editing window, which means f(x) = x^3, and press enter. Is the graph of of the reversed pairs (in red) that of a function? If it is, it has to be the graph of the inverse of f. Find a formula for the graph of the inverse of f.
Exercies: Use the graphing calculator above (applet) to determine which of theses functions have inverses and which do not have inverses.
1 - f(x) = x^4
2 - f(x) = sin(x)
3 - f(x) = ln(x)
4 - f(x) = exp(x)
5 - f(x) = 5
6 - f(x) = arcsin(x)
Solutions to above exercies
1 - f(x) = x^4 has no inverse, it is not a one to one.
2 - f(x) = sin(x) has no inverse, it is not a one to one.
3 - f(x) = ln(x) has an inverse: exp(x)
4 - f(x) = exp(x) has an inverse: ln(x)
5 - f(x) = 5 has no inverse, it is not a one to one.
6 - f(x) = arcsin(x) has an inverse: sin(x) with restricted domain -pi/2 > x > pi/2
More references on inverse functions and graphing calculators.
Inverse Function Definition.
More Graphing Calculators.