1 / 7

Lesson 2.3 Arithmetic Combinations of Functions

Lesson 2.3 Arithmetic Combinations of Functions. p. 90. In this section we will show how combinations of familiar functions together with some function operations can be used to construct more complex functions. Arithmetic Combinations of Functions.

bridie
Télécharger la présentation

Lesson 2.3 Arithmetic Combinations of Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Lesson 2.3 Arithmetic Combinations of Functions p. 90

  2. In this section we will show how combinations of familiar functions together with some function operations can be used to construct more complex functions. Arithmetic Combinations of Functions If f and g are functions, then the functions f + g, f – g, f•g and f/g are defined by (f + g)(x) = f(x) + g(x) (f – g)(x) = f(x) – g(x) (f•g(x)) = f(x) • g(x) (f/g)(x) = f(x)/ g(x) Note: Both f(x) and g(x) must be defined for any of these arithmetic operations to be defined at x. In other words, the domains of f + g, f – g, f•g, f/g must consist of those real numbers that are common to both the domains of f and g.

  3. Ex 1: Let f and g be defined by the table below. Show that f and g are functions, and then find f + g, f – g, f•g, and f/g. x -3 -2 -1 0 1 2 3 f(x) -1 1 2 -3 0 7 5 g(x) 0 -2 4 8 -1 3 5 x f(x) g(x) (f + g)(x) (f – g)(x) (f•g)(x) (f/g)(x) -1 -1 3 -2 -11 1 4 0 0 -2 8 -24 0 21 25 • Not defined • ½ • ½ • 3/8 • 0 • 7/3 • 1 0 -2 4 8 -1 3 5 -3 -2 -1 0 1 2 3 -1 1 2 -3 0 7 5 -1 6 5 -1 10 10

  4. Ex 2: Let f(x) = and Find f + g, f – g, fg, f/g and give their domains. Solution: Write the domains of f(x) and g(x).

  5. Vertical Compression and Elongation of Graphs • For any constant c > 0, the basic shape of the graph of y = c•g(x) is the • same as the graph of y = g(x), but with a change in the vertical scale. • The domains of cg and g are the same and the graphs have the same • x-intercepts. 2. For c > 1, the graph of y = c•g(x) is a vertical elongation, and for 0 < c < 1 it is a vertical compression of the graph of y = g(x). • The graph of y = -g(x) is the reflection about the x-axis of the graph of • y = g(x). • For c < -1, the graph of y = c•g(x) is a vertical elongation and reflection • of the graph of y = g(x). • For -1 < c < 0, the graph of y = c•g(x) is a vertical compression and reflection • of the graph of y = g(x). Look at p. 86-87 at graphs with different values of c.

  6. Graphs of the Reciprocal Function be the reciprocal of g(x). Let 1. f(x) is undefined when g(x) = 0. 2. f(x) and g(x) have the same value when g(x) = 1 or g(x) = -1 3. f(x) and g(x) have the same sign. 4. The magnitude of f(x) is large when the magnitude of g(x) is small. 5. The magnitude of f(x) is small when the magnitude of g(x) is large.

  7. Ex 3: Use the graph of g(x) = x + 5 to determine the graph of On board.

More Related