Graphs of Functions

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Section 7.3
Graphs of Functions
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Graphs of Functions

• In this section we are going to look at named
  graphs that are functions.
• Names you will get very acquainted with are
• Linear Function
• Constant Equation
• Absolute Value Function
• Quadratic Function
• Rational Function
• Polynomial function

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Linear Function

• A function where the x value and y value do not
  have any powers.
• A straight line graph, with no curves
• Domain will ALWAYS be (-8, 8)
• Range will ALWAYS be (-8, 8)
• The three forms are
• Standard Form Ax By C
• Slope Intercept Form y mx b
• Point Slope Form y - y1 m(x - x1)

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Standard Form

• Standard Form is used for future algebra
  problems.
• Ax By C
• Where A, B, C are all rational numbers, no
  fractions or decimals.
• Where A needs to be a positive number.
• Some problems will be
• Addition Method CH 8
• Matrix Method CH 8

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Standard Form

• Example
• Write 2y 3/2 x in standard form
• 2y 3/2 x

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Slope Intercept Form

• The Slope Intercept Form is used for graphing
  the linear function.
• Y mx b
• m
• represents the slope
• Needs to be written in a fraction form
• Numerator is the up () and down (-) movement
• Denominator is the right () and left (-)
  movement
• b
• represents the y-intercept
• (0, b)

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Steps to Graph a Linear Equation

• 1. Write the equation is slope intercept form
• 2. Find the y-intercept, (0, b)
• 3. Plot the y-intercept (0,b).
• 4. Find the slope, m
• Write m as a fraction
• Numerator is the movement on the y-axis,
• up, - down
• Denominator is the movement on the x-axis,
• right, - down
• 5. Use the slope to create your other points.
• 6. Connect all the points with a line.
• 7. Label one axis and put all 6 arrows in

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Slope Intercept form

• Graph y (1/2) x 2
• Y intercept (0, 2)
• Slope (1/2) up 1 right 2

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Slope Intercept form

• Graph y -3x - 1
• Y intercept (0, -1)
• Slope -3 (-3/1) down 3 right 1
• (3/-1) up 3
  left 1

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Slope Intercept form

• Graph y -2x 3
• Y intercept
• Slope

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Slope Intercept form

• Graph -3y x - 9
• Y intercept
• Slope

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Point Slope form

• Point Slope form is used with word problems to
  find the equation of the line.
• y - y1 m(x - x1)
• Point 1 (x 1, y 1) will change to values
• Point 2 (x, y) left alone
• Slope m will change to a value

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Point - Slope Form

• Example
• Find the equation of the line if the slope is 3
  and it goes through the point (1, 2)
• y - y1 m(x - x1)
• Point 1 (x 1, y 1) (1, 2)
• Point 2 (x, y)
• Slope m 3
• y- 2 3(x-1)
• y 2 3x 3
• y 3x -1

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Point - Slope Form

• Example
• Find the equation of the line if the slope is -2
  and it goes through the point (-3, 1)
• y - y1 m(x - x1)
• Point 1 (x 1, y 1)
• Point 2 (x, y)
• Slope m

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Non-Linear Functions

• Constant Equation
• Y
• X
• Absolute Value Function
• f(x) x
• Quadratic Function
• f(x) x²
• Rational Function
• f(x) 1 / x
• Polynomial Function
• High degree powerwill see later in the semester

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Constant function

• A vertical or horizontal line through a given
  number.
• Vertical Line will have the equation x
• Horizontal Line will have the equation y

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Vertical Line

• Graph x 2
• 
  Domain
• 
  Range

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Horizontal Line

• Graph y 2
• 
  Domain
• 
  Range

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Absolute Value Function

• F(x) x

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Absolute Value Function

• F(x) x
• 
  Domain
• 
  Range

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Quadratic Function

• F(x) x²

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Quadratic Function

• F(x) x²
• Domain
• Range
• 
  

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Rational Function

• F(x) 1 / x

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Rational Function

• F(x) 1 / x
• 
  Domain
• 
  Range

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Homework

• 7, 9, 12, 15, 17, 20, 25, 32, 41, 46, 47, 64, 65