Presentation on theme: "One-to-One and Inverse Functions Section 3.5. Function and One-to-One Function- each value of x corresponds to only one y – value Use vertical line."— Presentation transcript:
Function and One-to-One Function- each value of x corresponds to only one y – value Use vertical line test on graph One-to-One Function- each x value corresponds to one y value (it’s a function) and no two x values correspond to the same y value Use the Horizontal Line Test If every horizontal line intersects the function at most in one place, then it is one-to-one
Decide if the relation is a function. If it is a function decide if it is one-to-one. xy 24 35 37 xy 24 35 45 xy 24 35 47 Not a function Function, but not one-to-one Function and one-to-one
Decide if the relation is a function and one-to-one Not a function (Doesn’t pass vertical line test) Function and one- to-one (Passes vertical and horizontal line test) Function, but not one-to-one (Passes vertical, but not horizontal line test)
Inverse Function If a function is one-to-one, then it is possible to map each y value back to the x value. f(x) is the original function f - ¹(x) is the inverse function (read “f inverse”) To verify two functions are inverses of each other: f(f - ¹(x)) = x and f - ¹(f(x)) = x
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