Part 3/5:
For example, consider the graph of ( y = x^2 ). A horizontal line drawn at any positive ( y ) value will intersect the graph at two points, showing that this function does not meet the one-to-one criterion. Therefore, it cannot have an inverse.
Exploring Non-One-to-One Functions
In contrast, some functions, such as the sine function, exhibit periodic behavior and are inherently not one-to-one. The sine function oscillates between -1 and 1 indefinitely. When we apply the horizontal line test to the sine function, it is evident that many ( x ) values correspond to the same ( y ) value, which confirms that it is not one-to-one.