# 1140 L9 - y=f(x) x1 x2

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Lecture 9: Section 1.5 Analyzing Graphs of Functions The graph of a function y = f ( x ) is the set of points ( x; y ) in the xy -plane that satisfy the equation. ex. Which of the following graphs represent y as a function of x ? Find the domain and range of each function. 1) y = 2 2) x = ± 1

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3) y = x 2 4) x = y 2 Vertical Line Test for Functions A set of points in the xy -plane is the graph of y as a function of x if and only if no vertical line intersects the graph at more than one point. ex. Does the graph below represent a function?
NOTE: A function can have, at most, one y ± intercept. Zeros of a Function Def. The zeros of a function f ( x ) are the x - values for which ex. Find the zeros of each function. 1) f ( x ) = x 3 ± x 2 ± 4 x + 4 2) g ( x ) = p 4 ± x 2 3) h ( x ) = 1 ± 2 x 1 + 3 x

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Increasing and Decreasing Functions Def. A function f is increasing on an open interval I if for any x 1 and x 2 in I , if x 1 < x 2 , then Def. A function f is decreasing on an open interval I if for any x 1 and x 2 in I , if x 1 < x 2 , then Def. A function f is constant
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## This note was uploaded on 07/08/2011 for the course MAC 1140 taught by Professor Williamson during the Spring '08 term at University of Florida.

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1140 L9 - y=f(x) x1 x2

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