Chapter 2 - Graphing Linear Relations and Functions

Chapter 2 - Graphing Linear Relations and Functions

Functions, Relations, Domain, & Range Relation: a set of ordered pairs Domain: the set of x-coordinates Range: the set of y-coordinates When writing the domain and range, do not repeat values.

Relations and Functions Given the relation: {(2, -6), (1, 4), (2, 4), (0,0), (1, -6), (3, 0)} State the domain: D: State the range: R:

Relations and Functions Relations can be written in several ways: ordered pairs, tables, graphs, or mapping. We have already seen relations represented as ordered pairs. Table

{(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} x 3 7 0 -2 -5 3

y 4 2 -1 2 0 3 Mapping

Create two ovals with the domain on the left and the range on the right. Elements are not repeated. Connect elements of the domain with the corresponding elements in the range by drawing an arrow. Mapping {(2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)}

Functions A function is a relation in which the members of the domain (x-values) DO NOT repeat. So, for every x-value there is only one y-value that corresponds to it. y-values can be repeated.

Do the ordered pairs represent a function? Ex. 1 {(3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3, 3)} Ex. 2 {(4, 1), (5, 2), (8, 2), (9, 8)} Graphs of a Function Vertical Line Test:

If a vertical line is passed over the graph and it intersects the graph in exactly one point, the graph represents a function. Does the graph represent a function? If so, name the domain and range. x Yes or No

D: R: x Yes or No D: R: y

y Does the graph represent a function? If so, name the domain and range. x Yes or No D: R:

x Yes or No D: R: y y

Does the graph represent a function? If so, name the domain and range. x Yes or No D: R: x

Yes or No D: R: y y Function Notation

When we know that a relation is a function, the y in the equation can be replaced with f(x). f(x) is simply a notation to designate a function. It is pronounced f of x. The f names the function, the x tells the variable that is being used. Value of a Function

Since the equation y = x - 2 represents a function, we can also write it as f(x) = x - 2. Find f(4): Value of a Function If g(s) = 2s + 3, find g(-2). Value of a Function If h(x) = 4x2 3x + 1, find h(-2)

Find the Domain & Range when given the Equation 1.) f(x) = 1/4x 5 2.) f(x) = (x 3)2 3.) f(x) = |x| - 4 4.) f(x) = -x2 + 3

Recently Viewed Presentations

  • The Concept of Discourse Community: Star, Problem Child, Cash ...

    The Concept of Discourse Community: Star, Problem Child, Cash ...

    The Concept of Discourse Community: Star, Problem Child, Cash-cow or Dog? John M. Swales. ... Utilizes and possesses one or more genres in the communicative furtherance of its aims. 5) in addition to owning genres, it has acquired some specific...
  • Performance - Institute of Computer Engineering (E191)

    Performance - Institute of Computer Engineering (E191)

    Bitcoin Mining "We should have a gentleman's agreement to postpone the GPU arms race as long as we can for the good of the network." - Satoshi Nakamoto, Dez 2009
  • Presentation on Gas Turbine Instrumentation

    Presentation on Gas Turbine Instrumentation

    Presentation on Gas Turbine Instrumentation * * What is Hardware ? Hardware is an electronic circuit arranged in a specific fashion called a module or a card This card performs specific functions as directed by the software The required software...
  • Price Vs. Usage Variance Analysis

    Price Vs. Usage Variance Analysis

    Multiplying the unit cost delta times the 17 actual units, we get a $680 price variance. Summing the two, we reconcile to the $2,680 favorable net variance. In the third scenario, by identifying an alternate source, the contractor was able...
  • Phylum Platyhelmenthes Planarians, Flukes, & Tapeworms

    Phylum Platyhelmenthes Planarians, Flukes, & Tapeworms

    Tapeworms cont'd… Phylum Platyhelmenthes Planarians, Flukes, & Tapeworms Simple acoeleomates Bilaterally symmetrical Most flattened "Dorsoventrally" Divided into 4 classes: Class Turbellaria Planarian and assorted marine flatworms… Class Trematoda (Flukes) Similar in form to turbillarians Many are parasitic.
  • Vrtused ja vastutus Margit Sutrop Eesti hisvrtused Vrtuste

    Vrtused ja vastutus Margit Sutrop Eesti hisvrtused Vrtuste

    Juhtrühm: Margit Sutrop, Äli Leijen, Margus Pedaste, Katrin Poom-Valickis, Martin Ehala, Heli Mattisen, Triin Vihalemm, Toivo Maimets, Indrek Lillemägi, Toomas Kruusimägi, Martti Martinson, Ain Tõnisson Tartu Ülikooli eetikakeskuse töögrupp: Halliki Harro-Loit, Mari-Liis Nummert, Mari-Liisa Parder, Õnne Allaje, Nelli Jung, Katrin...
  • Windows Crash Data Collection and Analysis

    Windows Crash Data Collection and Analysis

    Windows Crash Analysis Results Archana Ganapathi Department of EECS, UC Berkeley ([email protected]) Motivation (1) "If a problem has no solution, it may not be a problem, but a fact, not to be solved, but to be coped with over time."...
  • 1 Objektif Menggunakan gambarajah serakan bagi menggambarkan perkaitan

    1 Objektif Menggunakan gambarajah serakan bagi menggambarkan perkaitan

    Sekiranya nilai se = 0, kita jangkakan bahawa titik-titik data akan berada di atas garisan regresi dan kita akan ada persamaan regresi sempurna. * Ralat piawai anggaran, se boleh diperolehi dengan menggunakan formula berikut: * Contoh 5 Kira nilai ralat...