1 / 14

Section 3.4

Section 3.4. Objectives: Find function values Use the vertical line test Define increasing, decreasing and constant functions Interpret Domain and Range of a function Graphically and Algebraically. * f(w) * f(x) * f(z) * f(5) * 3 * 4 * - 9. x * z *

fremont
Télécharger la présentation

Section 3.4

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. Section 3.4 • Objectives: • Find function values • Use the vertical line test • Define increasing, decreasing and constant functions • Interpret Domain and Range of a function Graphically and Algebraically

  2. * f(w) * f(x) * f(z) * f(5) * 3 * 4 * - 9 x * z * w * 5 * D Function: A function f is a correspondence from a set D to a set E that assigns to each element x of Dexactly one value ( element ) y of E f Graphical Illustration E f is a function

  3. More illustrations…. * f(w) * f(x) * f(z) * f(5) * 3 * 4 * - 9 * f(w) * f(x) * f(z) * f(5) * 3 * 4 * - 9 x * z * w * 5 * x * z * w * 5 * E E D D f is not a function Why? x in D has two values f is not a function Why? x in D has no values

  4. Note: f ( a + b ) f( a ) + f ( b ) Find function values Example 1: Let f be the function with domain R such that f( x) = x2 for every x in R. ( i ) Find f ( -6 ), f ( ), f( a + b ), and f(a) + f(b) where a and b are real numbers. Solution:

  5. Vertical Line Testof functions Vertical Line test: The graph of a set of points in a coordinate plane is the graph of a function if every vertical line intersects the graph in at most one point Example: check if the following graphs represent a function or not Function Function Not Function Function

  6. y y y f(x2) f(x1) f(x1) f(x2) f(x1) f(x2) x2 x2 x2 x1 x1 x1 x x x Increasing, Decreasing and Constant Function

  7. Example 1: Identify the interval(s) of the graph below where the function is • Increasing • Decreasing Solution: (a) Increasing (b) Decreasing:

  8. Example 2: Sketch the graph that is decreasing on ( ,- 3] and [ 0, ), increasing on [ -3 ,0 ], f(-3) = 2 and f (2 ) = 0 Solution: decreasing increasing decreasing -3 0

  9. Interpretation of Domain and Rangeof a function f f Domain is the Set of all x where f is well defined Range is the set of all values f( x ) Where x is in the domain

  10. Graphical Approach toDomain and Range Example 1: Find the natural domain and Range of the graph of the function f below Range The functionf represents f (x ) = x2. f is well defined everywhere in R. Therefore, Domain = R Every value of f is non-negative ( greater than or equal to 0. Therefore , Range = Domain

  11. More illustrations of Domain and Range of a graph of a function f This graph does not end on both sides Domain = Range = These two graphs seem similar, but the domain and range are different This graph ends, it is also not defined at x = –2 and well defined at x =2 Domain = Range =

  12. Class Exercise 1 Find the natural domain and range of the following graphs Domain = Range = Domain = Range = Domain = Domain = Range = Range =

  13. Algebraic Approach to find theDomain of a function f Example 1: Find the natural domain of the following functions Solution: ( 1 ) f is a linear function. f is well-defined for all x. Therefore, Domain = R ( 2 ) f is a square root function. f is well defined when Domain = (3) f is well defined when Domain = and (4) f is well defined when Domain = -5

  14. Do all the Homework assigned in the syllabus for Section 3.4

More Related