3.2 Graphs of Functions

3.2 Graphs of Functions - Graphs of Functions Graphs of...

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Unformatted text preview: Graphs of Functions Graphs of Functions Section 3.2 Vertical Line Test Vertical Line Test A graph in a coordinate plane represents a function iff no vertical line intersects the graph more than once. Function Not a Function Increasing and Decreasing Increasing and Decreasing A function is said to be increasing if its graph rises as you move from left to right over the interval. A function is said to be decreasing if it falls as you move from left to right over the interval. A function is constant if its graph is a horizontal line. increasing decreasing constant Local Maxima and Minima Local Maxima and Minima A function has a local maximum at x = c if the graph of has a peak at the point (c, f(c)). Similarly, a function has a local minimum at x = d if the graph of f has a valley at (d, f(d)). maximum minimum Concavity and Inflection Points Concavity and Inflection Points Concavity is used to describe the way that a curve bends. A point where the curve changes concavity is called an inflection point. Concave up Concave down Inflection point Piecewise Function Piecewise Function The graphs of piecewise­defined functions are often discontinuous, that is, they commonly have jumps or holes. To graph a piecewise­ defined function, graph each piece separately. x2 if x ≤ 1 f ( x) = x + 2 if 1 < x ≤ 4 1 4 Absolute Value Function Absolute Value Function f ( x) = x The Greatest Integer (Step) Function The Greatest Integer (Step) Function f ( x) = [ x ] Parametric Graphing Parametric Graphing In parametric graphing, the x­coordinate and the y­coordinate of each point are each given as a function f a third variable, t, called a parameter. To graph y = f(x) in parametric mode, let x = t y = f(t) To graph x = f(y) in parametric mode, let x = f(t) y = t Joke Time Joke Time How does a flea get from place to place? By itch­hiking! Issues, issues, issues, issues, issues, issues, issues, issues, issues, issues, what do you need next? Socks to go with the ten issues ...
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This note was uploaded on 12/01/2011 for the course MATH 111 taught by Professor Stuff during the Winter '11 term at BYU.

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