# 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. Your browser is completely ignoring the tag! 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.