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Chapter 8: Inverses and Radicals Lesson 2: Inverses of Relations Mrs. Parziale What is a Function? • A relation is a set of ordered pairs. • A function is a relation with ordered pairs whose x-coordinate has only one y-coordinate. • What test can you apply to the graph of a relation to see if it is a function? Vertical line test Function or Not? • Graph the following relation on the coordinate grid: f = { (1,4), ),(2, 8) , ( 3, 8), (0, 0), (1, -4)} • Is it a function? • Create a new function g by switching the x and y coordinates of f. g= • Is it a function? • What is the line of symmetry for f and g? Inverses Definition: The inverse of a relation is the relation obtained by reversing the order of the x and y coordinates in each ordered pair in the relation. • The domain of a relation is the set of all possible values for the x coordinate • The range of a relation is the set of all possible values of the y coordinate. • In the examples on the previous slides how do the domain of f and the range of g compare? • …the range of f and the domain of g? Inverse Relation Theorem Suppose f is a relation and g is the inverse of f. Then: 1) A rule for g can be found by switching x and y. 2) The graph of g is the reflection image of the graph of f over the line y=x 3) The domain of g is the range of f, and the range of g is the domain of f. Example 1 • Let g = { (4, 3), (0, -1), (5, 2), (-8, -1)} • a) Is g a function? Why of why not? • b) Identify the inverse of g. • c) Is the inverse of g a function? Why or why not? The inverse of a relation is always a relation. But the inverse of a function is not always a function . • Graph the function: y = 3x +2 • Complete the chart for coordinates on the graph. x (x,y) Inverse of y =3x + 2 (y,x) 0 1 -1 • Graph the inverse of y = 3x + 2 • What is the equation of the inverse of y = 3x +2 • Is the inverse a function? Theorem ( Horizontal Line Test for Inverses) The inverse of a function f is itself a function if and only if no horizontal line intersects the graph of f in more than one point. Determine if the inverse of a function is a function. Explain your reasoning. a) b) c) Closure • How can the inverse of a relation be found from the coordinates of the relation? • Explain how the graphs of any relation f an its inverse are related? • Give the equation for the inverse of the relations: y = 3x – 2 y = 9x2 +12x - 6

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posted: | 2/5/2013 |

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