04Gonetoonefuncs

= One-to-One Functions =

Recall that
 * A one-to-one function has the following restrictions
 * for any x value, it has only one y value
 * ie it passes the vertical line test
 * for any y value, it has only one x value
 * ie it passes a horizontal line test


 * If a function is continuous, the only way it can be a one-to-one function is if
 * it is an Increasing Function
 * gradient is always greater than or equal to zero
 * m = 0 at stationary points only
 * or it is a Decreasing Function
 * gradient is always less than or equal to zero
 * m = 0 at stationary points only

Functions with restricted domains


 * Sometimes, we are asked to restrict the domain of a function to make it a one-to-one function
 * Usually, the question asks for the maximal restricted domain
 * ie the largest possible restricted domain that makes it a one-to-one function


 * When asked to do so, there will often be multiple possible answers

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