One-to-One Functions;

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Presentation transcript:

One-to-One Functions; Section 6.2 One-to-One Functions; Inverse Functions

OBJECTIVE 1

(a) NO (b) {(1,5), (2,8), (3,11), (4,14)} YES Student Car Dan John Joe Andy Saturn Pontiac Honda NO YES

For each function, use the graph to determine whether the function is one-to-one. (a) (b) YES NO

A function that is increasing on an interval I is a one-to-one function in I. A function that is decreasing on an interval I is a one-to-one function on I.

OBJECTIVE 2

Find the inverse of the following function Find the inverse of the following function. Let the domain of the function represent certain students, and let the range represent the make of that student’s car. State the domain and the range of the inverse function. Student Car Dan John Joe Michelle Saturn Pontiac Honda Chrysler …

{(1,5), (2,8), (3,11), (4,14)} State the domain and the range of the function and its inverse. Inverse: { (5,1), (8,2), (11,3), (14,4) } Function: Domain: { 1, 2, 3, 4 } Range: {5, 8, 11, 14 } Inverse Function: Domain: { 5, 8, 11, 14 } Range: {1, 2, 3, 4 }

OBJECTIVE 3

The graph shown is that of a one-to-one function The graph shown is that of a one-to-one function. Draw the graph of the inverse. (1,4) (0,3) (-1,0) …

OBJECTIVE 4

x = 1 Vertical asymptote y = 2 Horizontal asymptote y = 1 Horizontal asymptote x = 2 Vertical asymptote

Domain: { x | x ≠ -1 } Using f-1(x) = (x +1)/(x – 2) which has domain of { x | x ≠ 2 } implies range of f(x) is { y | y ≠ 2 } Since domain of f(x) is { x | x ≠ -1 } implies the range of f-1 is { y | y ≠ -1 }.

WHY x ≥ 1