ch.2 Functions

ch.2 Functions - Chapter 2 Functions 2.1 Input and Output...

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Chapter 2 Functions 2.1 Input and Output
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Key Points • Basic function interpretation and manipulation using standard function notation
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Finding Output Values: Evaluating a Function Example Let h ( x ) = x 2 + 2 x - 4. Evaluate and simplify the following expressions. (a) h (2) (b) h (a − 2) (c) h (a) − 2 (d) h (a) − h (2) Functions Modeling Change: A Preparation for Calculus, 4th
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Evaluating functionsFinding Input Values: Solving Equations Example 2 Suppose (a)Find f(3) (b)Find an x -value that results in f ( x ) = 3. (c)coordinates Functions Modeling Change: A Preparation for Calculus, 4th 1 ( ) 4 f x x = +
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Like 18
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Finding Output Values from Tables Example 8 The table shows the revenue, R = f ( t ), received, by the National Football League, NFL, from network TV as a function of the year, t , since 1975. (a) Evaluate and interpret f(25). (b) Solve and interpret f(t) = 364 Solution The table shows f (25) = 2200. Since t = 25 in the year 2000, we know that NFL’s revenue from TV was $2200 million in the year 2000. Functions Modeling Change: A Preparation for Calculus, 4th Year, t (since 1975) 0 5 10 15 20 25 30 Revenue, R (million $) 201 364 651 1075 1159 2200 2200
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Finding Input/Output Values from Graphs Exercise 35 (a) and (c) (a) Evaluate f(2) and explain its meaning . ( c) Solve f ( w ) = 4.5 and explain what the solutions means. Solution (a) f (2) ≈ 7, so 7 thousand individuals were infected 2 weeks after onset. (c) If you imagine a horizontal line drawn at f = 4.5, it would intersect the graph at two points, at approximately w = 1 and w = 10. This would mean that 4.5 thousand individuals were infected with influenza both one week and ten weeks after the Functions Modeling Change: A Preparation for Calculus, 4th An epidemic of influenza spreads through a city. The figure to the right shows the graph of I = f ( w ), where I is the number of individuals (in thousands) infected w weeks after the epidemic begins. w f ( w ) f
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Chapter 2 Functions 2.2 Domain and Range
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Key Points Domain and range of a function Using a graph to find the domain and range Finding domain and range algebraically
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Warm up S2 and S4 page 77
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Find the domain and range 11 ) ( - = t t h
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Using a Formula to Find the Domain and Range of a Function Example 4 State the domain and range of g , where g ( x ) = 1/ x . Solution The domain is all real numbers except those which do not yield an output value. The expression 1/x is defined for any real number x except 0 (division by 0 is undefined). Therefore, Domain: all real
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This note was uploaded on 04/04/2012 for the course MATH 2412 taught by Professor Staff during the Spring '08 term at Austin CC.

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ch.2 Functions - Chapter 2 Functions 2.1 Input and Output...

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