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Graphing Calculator For Inverse Functions


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.

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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.


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Updated: 2 April 2013

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