The equation of the line less than zero is y=-2x+2 if x is less than or equal to 0. The equation of the quarter circle is the square root of 4-x^2 if 0<x<2. The equation for the line greater than 2 is (x-2)^2 if x is greater than or equal to 2.
First I graphed the function y=x^2. In order to find the inverse of this function, switch the x and y, which leaves the function x=y^2. From this point, to get rid of a squared number or variable, take the square root of the squared variable or number. The end result: y equals the plus or minus square root of x. After graphing the inverse, I graphed the line y=x, showing the the inverse of all functions are reflected over this function. This was shown in the second photo where I folded my plastic piece along the function y=x. Although the function y=x^2 did not have an inverse that was a function, there are some functions that have inverse functions as well. For instance, the function y=x can have the inverse function of x=y. In order to tell if a graph is a function, it needs to pass the vertical line test. The vertical line test can be performed by taking any straight object and holding in to the graph upright. By moving the straight object to the left and right, it can be observed if the graph is a function. There can only be one y value for every x. This project was interesting to me because I learned if I need to find the inverse of a graph given, I can check my work by graphing the function y=x and reflect the graph over that line.
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April 2015
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