Graphing Lines

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Graphing Lines
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How To Find THE SLOPE of a Line Given Two Points
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Slope of a Line
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Slope of a Line
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Definition of Slope

• The slope of the line is its measure of
  steepness. It measures the rate of change of the
  line. In all lines the slope is constant, it
  doesnt change no matter where you are at on the
  line.

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Find the Slope of the line containing the points
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Bicycles
In groups, generate the line that relates the
number of wheels to the number of bicycles.
Represent it Graphically. What does the slope of
this line represent?
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Graph of a Line
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Intercepts

• Where the graph crosses the x-axis is the
  x-intercept. It has coordinates (a,0).
• Where the graph crosses the y-axis is the
  y-intercept. It has coordinates (0,b).

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The x and y intercepts of a line
y
y-intercept
(0,b)
x-intercept
x
(a,0)
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Example

• Find the x and y intercepts of the line given by

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Slope Intercept Form
y
x
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Determine the slope and y-intercept of the
following
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Point Slope Form
y
x
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Find the Equation of the Line Through the Points
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Line Formulas
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Definition of Function

• or
• How to Relate

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Definition of a Relation
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Relation
(A)
(B)
(C)

• 32 mpg
• 8 mpg
• 16 mpg

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Domain and Range

• The values that make up the set of independent
  values are the domain
• The values that make up the set of dependent
  values are the range.
• State the domain and range from the 4 examples of
  relations given.

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Domain
Range
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Definition of a Relation

• A Relation maps a value from the domain to the
  range. A Relation is a set of ordered pairs.
• The most common types of relations in algebra map
  subsets of real numbers to other subsets of real
  numbers.

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Example
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Definition of a Function

• If a relation has the additional characteristic
  that each element of the domain is mapped to one
  and only one element of the range then we call
  the relation a Function.

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Definition of a Function

• If we think of the domain as the set of boys and
  the range the set of girls, then a function is a
  monogamous relationship from the domain to the
  range. Each boy gets to go out with one and only
  one girl.
• But It does not say anything about the girls.
  They get to live in Utah.

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Decide if the Relation is a Function.

• The relation is the year and the cost of a first
  class stamp.
• The relation is the weight of an animal and the
  beats per minute of its heart.
• The relation is the time of the day and the
  intensity of the sun light.
• The relation is a number and its square.
• The relation is time since you left your house
  for work and your distance from home.

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Examples Please

• Give three examples from the real world of
  relations. Be sure and state the domain, the
  range, and the definition of how the variables
  are related.
• Decide which if any of your examples are
  functions.

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NOT A FUNCTION
R
x
DOMAIN
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FUNCTION
f
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Mathematical Examples

• Decide if the following relations are functions.

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Ways to Represent a Function

• Symbolic

• Graphical

• Numeric

• VerbalThe cost is twice the original amount.

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Function NotationThe Symbolic Form

• A truly excellent notation. It is concise and
  useful.

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(No Transcript)
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Examples of Function Notation

• The f notation
• Find f(2), g(-1), f(-0.983),

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Your Turn!
Given
Evaluate the following
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Graphical Representation

• Graphical representation of functions have the
  advantage of conveying lots of information in a
  compact form. There are many types and styles of
  graphs but in algebra we concentrate on graphs in
  the rectangular (Cartesian) coordinate system.

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Graphs and Functions
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Determine the Domain and Range for Each Function
From Their Graph
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Vertical Line Test for Functions

• If a vertical line intersects a graph once and
  only once for each element of the domain, then
  the graph is a function.

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How to determine Domain and Range of a function.

• Graph the following on your calculator. Also give
  the algebra.

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Big Deal!

• A point is in the set of ordered pairs that make
  up the function if and only if the point is on
  the graph of the function.

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Key Points

• Definition of a function
• Ways to represent a functionSymbolicallyGraphica
  llyNumericallyVerbally