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Chapter 2 (F11)

# Chapter 2 (F11) - Section 2.1 Basics of Functions and Their...

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Section 2.1 – Basics of Functions and Their Graphs Relation – Any set of ordered pairs. In relations, there is a correspondence between 2 sets: The domain (first components) and The range (second components) Function – A relation where each element of the domain corresponds to exactly one element of the range. Example : Determine if the following relations represent functions. a) Domain Range 2 3 4 5 6 7 b) { (2, 4), (1, 3), (–2, 3), (1, 4) } x is called the “ input ” and is an independent variable because it can be any number in the domain. y is called the “ output ” and is a dependent variable because its value depends on x . 1

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Function Notation: ( ) y f x = means that y is a function of x . ( ) f x is read as “ f of x or f at x and represents the value of the function at the number x . If x and y are related so that y = x 2 – 2 , we can say 2 ( ) 2 f x x = - . Example : Find the following function values for the function 2 ( ) 2 f x x = - : a) f (0) = b) f (–3) = c) f (– x ) = d) f (2 x ) = e) f ( x – 1) = f) f ( x + h ) = g) f ( x ) = 2
Vertical Line Test If any vertical line intersects a graph in more than one point, then the graph does not represent a function. Examples : Are the following graphs the graphs of functions? Obtaining Information from the graph of a function : • A closed dot indicates that the graph does not extend beyond this point and that the point belongs to the graph. ◦ An open dot indicates that the graph does not extend beyond this point and that the point does not belong to the graph. An arrow indicates that the graph extends indefinitely in the direction of the arrow. 3

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Example : a) What is the domain of f ? b) What is the range of f ? c) Find f (0) = d) Find f (2) = e) For which value(s) of x is f ( x ) = 2? f) What are the x -intercepts? g) What are the y -intercepts? 4
Example : a) What is the domain? b) What is the range? c) Find the x and y intercepts d) Find f (1) = e) Find f (3) = 5

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Section 2.2 – More on Functions and Their Graphs The Difference Quotient : ( ) ( ) , 0 f x h f x h h + - Steps : 1. Calculate ( ) f x h + first 2. Subtract ( ) f x from ( ) f x h + 3. Divide by h Example : Evaluate the difference quotient when ( ) 2 5 f x x = + . Example : Evaluate the difference quotient when 2 ( ) 4 3 f x x x = - + - . Increasing, Decreasing, and Constant: 6
: List the domain and the interval(s) where the graph is increasing, decreasing, and constant. Use interval notation.

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Chapter 2 (F11) - Section 2.1 Basics of Functions and Their...

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