1 / 12

Coming after you with Ch. 2: Functions and Their Graphs 2.1: Functions Learning Targets:

Coming after you with Ch. 2: Functions and Their Graphs 2.1: Functions Learning Targets: Determine Whether a Relation Represents a Function Find the Value of a Function…plug it in, plug it in! Find the Domain if a Function…look at the x’s ! Identify the Graph of a Function

aladdin-reed
Télécharger la présentation

Coming after you with Ch. 2: Functions and Their Graphs 2.1: Functions Learning Targets:

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. Coming after you with Ch. 2: Functions and Their Graphs • 2.1: Functions • Learning Targets: • Determine Whether a Relation Represents a Function • Find the Value of a Function…plug it in, plug it in! • Find the Domain if a Function…look at the x’s! • Identify the Graph of a Function • Obtain Information from the Graph of a Function

  2. Let X and Y be two nonempty sets of real numbers. A function from X into Y is a rule or a correspondence that associates with each element of X a unique element of Y. The set X is called the domain of the function. For each element x in X, the corresponding element y in Y is called the image of x. The set of all images of the elements of the domain is called the range of the function.

  3. f x y x y x X Y RANGE DOMAIN

  4. Determine which of the following relations represent functions. Not a function. Function. Function.

  5. Not a function. (2,1) and (2,-9)both work.

  6. Find the domain of the following functions: A) B) With a rational expression be sure to consider all values that may make it undefined.

  7. C) Even roots are real only for nonnegative numbers.

  8. Theorem: Vertical Line Test A set of points in the xy - plane is the graph of a function if and only if a vertical line intersects the graph in at most one point.

  9. y x Not a function.

  10. y x Function.

  11. Determine the domain, range, and intercepts of the following graph. Find f(1). How often does the line y=-1 intersect the graph? For what value does f(x)=3? y 4 (2, 3) (10, 0) 0 (4, 0) (1, 0) x (0, -3) -4

  12. Finding values of a function For the function defined by f(x) = x2 - 2x, evaluate: (a) f(2) (b) f(x) + f(2) (c) f(x+2)(d) f(x+h) (a) f(2) = 22-2(2) = 0 (b) f(x) + f(2) = x2 - 2x + 0 (c) f(x+2) = (x+2)2 - 2(x + 2) = x2 + 4x + 4 - 2x - 4 = x2 + 2x (d) f(x+h) = (x + h)2 - 2(x + h) = x2 + 2xh + h2 - 2x - 2h

More Related