Presentation is loading. Please wait.

Presentation is loading. Please wait.

CHAPTER 2: More on Functions

Similar presentations


Presentation on theme: "CHAPTER 2: More on Functions"— Presentation transcript:

1

2 CHAPTER 2: More on Functions
2.1 Increasing, Decreasing, and Piecewise Functions; Applications 2.2 The Algebra of Functions 2.3 The Composition of Functions 2.4 Symmetry and Transformations 2.5 Variation and Applications Copyright © 2009 Pearson Education, Inc.

3 2.2 The Algebra of Functions
Find the sum, the difference, the product, and the quotient of two functions, and determine the domains of the resulting functions. Find the difference quotient for a function. Copyright © 2009 Pearson Education, Inc.

4 Sums, Differences, Products, and Quotients of Functions
If f and g are functions and x is in the domain of each function, then Copyright © 2009 Pearson Education, Inc.

5 Copyright © 2009 Pearson Education, Inc.
Example Given that f(x) = x + 2 and g(x) = 2x + 5, find each of the following. a) (f + g)(x) b) (f + g)(5) Solution: a) b) We can find (f + g)(5) provided 5 is in the domain of each function. This is true. f(5) = = 7 g(5) = 2(5) + 5 = 15 (f + g)(5) = f(5) + g(5) = = 22 or (f + g)(5) = 3(5) + 7 = 22 Copyright © 2009 Pearson Education, Inc.

6 Copyright © 2009 Pearson Education, Inc.
Another Example Given that f(x) = x2 + 2 and g(x) = x  3, find each of the following. a) The domain of f + g, f  g, fg, and f/g b) (f  g)(x) c) (f/g)(x) Solution: a) The domain of f is the set of all real numbers. The domain of g is also the set of all real numbers. The domains of f + g, f  g, and fg are the set of numbers in the intersection of the domains—that is, the set of numbers in both domains, or all real numbers. For f/g, we must exclude 3, since g(3) = 0. Copyright © 2009 Pearson Education, Inc.

7 Another Example continued
b) (f  g)(x) = f(x)  g(x) = (x2 + 2)  (x  3) = x2  x + 5 c) (f/g)(x) = Remember to add the stipulation that x  3, since 3 is not in the domain of (f/g)(x). Copyright © 2009 Pearson Education, Inc.

8 Copyright © 2009 Pearson Education, Inc.
Difference Quotient The ratio below is called the difference quotient, or average rate of change. Copyright © 2009 Pearson Education, Inc.

9 Copyright © 2009 Pearson Education, Inc.
Example For the function f given by f (x) = 5x  1, find the difference quotient Solution: We first find f (x + h): Copyright © 2009 Pearson Education, Inc.

10 Copyright © 2009 Pearson Education, Inc.
Example continued Copyright © 2009 Pearson Education, Inc.

11 Copyright © 2009 Pearson Education, Inc.
Another Example For the function f given by f (x) = x2 + 2x  3, find the difference quotient. Solution: We first find f (x + h): Copyright © 2009 Pearson Education, Inc.

12 Copyright © 2009 Pearson Education, Inc.
Example continued Copyright © 2009 Pearson Education, Inc.


Download ppt "CHAPTER 2: More on Functions"

Similar presentations


Ads by Google