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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- Winter '11
- Calculus, Order theory, Monotonic function, Convex function, vertical line test