1 Functions 2 (No Transcript) 3 Representations of Functions
There are four possible ways to represent a function
verbally (by a description in words)
numerically (by a table of values)
visually (by a graph)
algebraically (by an explicit formula)
A The area of a circle depends on the radius of the circle. The rule that connects and is given by the equation
With each positive number there is associated one value of and we say that is a function of
4 B C 5 The rule that the U. S. Postal Service used as of 2001 is as follows The cost is 34 cents for up to one ounce plus 22 cents for each successive ounce up to 11 ounces. D 6 Graphs of Functions
The graph of a function is a curve in the -plane. But the question arises Which curves in the -plane are graphs of functions This is answered by the following test.
The Vertical Line Test A curve in the -plane is the graph of a function of if and only if no vertical line intersects the curve more than once.
7 Classification of Functions
We may classify functions by their formula as follows
Linear Functions Quadratic Functions. Cubic Functions.
Piecewise Defined Functions
Absolute Value Functions Step Functions
Trigonometric and Inverse trigonometric Functions
8 Functions Properties
We may classify functions by some of their properties as follows
Injective (One to One) Functions
Surjective (Onto) Functions
Odd or Even Functions
Increasing and Decreasing Functions
9 Symmetry 10 Transformations of Functions 11 Combinations of Functions 12 Composition of Functions 13 (No Transcript) 14 (No Transcript) 15 Power Functions 16 Exponential Functions 17 Inverse Functions 18 (No Transcript) 19 (No Transcript) 20 Logarithmic Functions 21 The logarithm with base is called the natural logarithm and has a special notation 22 When we try to find the inverse trigonometric functions we have a slight difficulty. Because the trigonometric functions are not one-to-one they dont have inverse functions. The difficulty is overcome by restricting the domains of these functions so that hey become one-to-one. Inverse Trigonometric Functions 23 (No Transcript) 24 (No Transcript)
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