21: Graphing Linear Relations and Functions - PowerPoint PPT Presentation

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21: Graphing Linear Relations and Functions

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A function is a relation in which the members of the domain (x-values) DO NOT repeat. ... equation y = x - 2 represents a function, we can also write it as f ... – PowerPoint PPT presentation

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Title: 21: Graphing Linear Relations and Functions


1
2-1 Graphing Linear Relations and
Functions
  • Objectives
  • Understand, draw, and determine if a relation
    is a function.
  • Graph write linear equations, determine
    domain and range.
  • Understand and calculate slope.

2
Relations Functions
  • 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.

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

4
Relations and Functions
  • Relations can be written in several ways ordered
    pairs, table, graph, or mapping.
  • We have already seen relations represented as
    ordered pairs.

5
Table
  • (3, 4), (7, 2), (0, -1),
  • (-2, 2), (-5, 0), (3, 3)

6
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.

7
Mapping
  • (2, -6), (1, 4), (2, 4), (0, 0), (1, -6), (3, 0)

8
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.

9
Functions
  • Discrete functions consist of points that are
    not connected.
  • Continuous functions can be graphed with a line
    or smooth curve and contain an infinite number
    of points.

10
Do the ordered pairs represent a function?
  • (3, 4), (7, 2), (0, -1), (-2, 2), (-5, 0), (3,
    3)
  • No, 3 is repeated in the domain.
  • (4, 1), (5, 2), (8, 2), (9, 8)
  • Yes, no x-coordinate is repeated.

11
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.

12
Does the graph represent a function? Name the
domain and range.
  • Yes
  • D all reals
  • R all reals
  • Yes
  • D all reals
  • R y -6

13
Does the graph represent a function? Name the
domain and range.
  • No
  • D x 1/2
  • R all reals
  • No
  • D all reals
  • R all reals

14
Does the graph represent a function? Name the
domain and range.
  • Yes
  • D all reals
  • R y -6
  • No
  • D x 2
  • R all reals

15
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.

16
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)
  • f(4) 4 - 2
  • f(4) 2

17
Value of a Function
  • If g(s) 2s 3, find g(-2).
  • g(-2) 2(-2) 3
  • -4 3
  • -1
  • g(-2) -1

18
Value of a Function
  • If h(x) x2 - x 7, find h(2c).
  • h(2c) (2c)2 (2c) 7
  • 4c2 - 2c 7

19
Value of a Function
  • If f(k) k2 - 3, find f(a - 1)
  • f(a - 1)(a - 1)2 - 3
  • (Remember FOIL?!)
  • (a-1)(a-1) - 3
  • a2 - a - a 1 - 3
  • a2 - 2a - 2
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