Functions 4 Reciprocal & Rational Functions

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Presentation transcript:

Functions 4 Reciprocal & Rational Functions Composite & Inverse Functions Homework (Haese & Harris, 3rd edition) Ex 3F Q6 p97 Ex 4G Q1, 4 p129

The Reciprocal Function Reciprocal Functions are functions of the form: All reciprocal functions hare the same shape * Vertical Asymptote is found by letting the denominator equal zero. ie. x = 0 * Horizontal Asymptote is found by allowing x to become very large (both positive and negative) ie. as as The reciprocal function is its own inverse, or it is called a self-inverse

Examples

Rational Functions y = 0 (x-axis) Same rules for asymptotes as discussed for the reciprocal function. Rational Functions of the Form Rational Functions of the Form Vertical Asymptote: Vertical Asymptote: y = 0 (x-axis) Horizontal Asymptote: Horizontal Asymptote: Example: Example: Horizontal Asymptote: Vertical Asymptote: Domain: Range: Sketch Horizontal Asymptote: Vertical Asymptote: Domain: Range: Sketch

Composite Functions 3: 1: 2:

Inverse Functions Graphically - The inverse of a function is found by reflecting the function through the line y = x. You can use the horizontal line test to predict if the inverse function exists. If a horizontal line crosses the graph of a function more than once, there is no inverse function. since the inverse interchanges the x and y values of the function, it also interchanges the domain and range! Which of the following graphs have inverses that are functions?

Graphical Examples of Functions and their Inverses

Finding Inverses of Functions Algebraically Examples: Find the inverses of the following functions: a. b.