Functions and Coordinate Plane

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Functions and Coordinate Plane

• Section 1.1

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Domain and Range

• Domain - all possible x values.
• Range - all possible y values.
• Ordered pair (x,y)

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CEFind the domain and range in the set

• (0,0),(1,2),(2,4),(2,6),(4,8)
• Domain
• Range

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Coordinate Plane

• Cartesian Coordinate System
• Has 4 quadrants
• Note where x and y are positive and negative.

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CE

• Graph the following relations. Find the domain
  and range of each.

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Function Definition

• A relation in which each member of the domain is
  paired with exactly one member of the range.

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CE State if each is a function.

• A. (1,2),(2,3),(3,4)
• B. (4,4),(2,3),(4,2),(3,4)

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CE Determine which set is a function

• A. (1,2), (1,5), (3,7)
• B. (4,5), (3,5),(2,6), (1,7)

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CE For the function

• Find
• A f(-3)
• B f(0)

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CEfor the function

• Find
• A f(16)
• B f(2/3)

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CESubstituting into a function

• Find f(3)

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CESubstituting into a function

• Find f(2)

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CE

• Evaluate
• f(x h)-f(x)
• h

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CEDetermine which real numbers must be excluded
from the domain of each function.

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Determine if y is a function of x
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CE

• Is y a function of x?

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CE

• Is y a function of x?

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Page 92

• 1 9 odd
• 11,13,14
• 22 28 even
• 39,40

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Section 2

• Graphing Lines in the Cartesian Coordinate Plane

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Terms

• Ordered pair (x,y)
• Abscissa- another name for the x term
• Ordinate- another name for the y term

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• A linear equation is an equation whose largest
  exponent is one.
• The equation of a straight line is called a
  linear equation.
• Example of a linear equation
• y 3x 2

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CE

• Graph the linear equation using an x,y chart
• y x 2

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Intercepts

• The x intercept of a graph is where the graph
  intersects the x axis
• The y intercept of a graph is where the graph
  intersects the y axis.

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To Find the X intercept

• Let y 0 and solve for x.

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CE

• Find the x intercept of
• y 2x 1

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To find the y intercept

• Let x 0 and solve for y.

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CE

• Find the y intercept
• y 2x 1

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CE

• Graph using the intercepts
• 2x 2y 4

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Definition of Slope

• If two points (x1,y1) and (x2, y2) are on a line
  l, then the slope m of l is defined by

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CE

• Find the slope of a line determined by the points
  (-3,4) and (1,-6)

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CE

• Find the slope of a line determined by the points
  (2,5) and (3,4)

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CE

• Draw the line through point ( -2,2) and has a
  slope of

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CE

• Draw the line through point ( 2,4) and has a
  slope of

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Page 99

• Test your understanding 1 - 6

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Summary of Slope

• Slope can be positive
• Slope can be negative
• Slope can be 0
• Slope can be undefined

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CE

• Give an equation to represent a line with each
  slope.
• Positive slope
• Negative slope
• 0 slope
• Undefined slope

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Page 102 104

• 2 12 even
• 22 34 even
• 37

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Section 2.3

• Algebraic Forms of Linear Functions

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Slope Intercept form of a line

• Y mx b
• b is the y intercept
• m is the slope.

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CE

• Graph the linear function
• f(x) 2x - 1

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CE

• Write, in slope-intercept form, the equation of
  the line with slope 2/3 passing through the point
  (0,-5).

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Point Slope Form of a line

• Where m is the slope and

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CE

• Write the point-slope form of the line l with
  slope m 3 that passes the point (-1,1).

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CE

• Write the point-slope form of the line l with
  slope m 1 that passes the point (5,-2/3).

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Page 110

• 1 - 9

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CE

• Write the slope-intercept form of the line
  through the two points(6,-4) and (-3,8)

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Recall

• Perpendicular lines have slopes that are negative
  reciprocals of one another.

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CE

• What is the opposite reciprocal of

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CE

• Write an equation of the line that is
  perpendicular to the line 5x 2y 2 and that
  passes through the point (-2,-6).

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CE

• Write an equation of the line that is
  perpendicular to the line y 3x 1 and that
  passes through the point (4,7).

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General Liner Equation

• Ax By C
• Where A,B,C are constants and A,B are not both 0.

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CE

• Find the equation of the line through the points
  (2,-3) and (3,-1).
• Write the equation
• In point slope
• In slope intercept form
• In general form

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• 1 9
• 23 - 29

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Page 113

• 10 2232 40 all even
• 41,42,43

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Sections 2.5

• Systems of equations

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Note

• When you solve a system you are looking for the
  point of intersection of two lines.

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To solve a system by substitution do the following

• Solve the first equation for y
• Substitute the solution for y into the second
  equation.
• Solve for x

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Cont.
Substitute the value for x into the first
original equation Solve for y You now have the
point of intersection
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Note

• If a false statement is encountered the system is
  inconsistent, the lines do not intersect.

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CE

• Solve the system by substitution
• 3x y 1
• 2x y 9

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CE

• Solve the system by substitution
• -2x y -1
• -6x 3y 12

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CE

• Solve the system by substitution
• -2x y 3
• 3x y -4

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CE

• 10,000 people attended a certain concert. Adult
  tickets were 5 and student tickets were 3. If
  35,000 worth of tickets were sold, how many
  adults ere at the concert?

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CE

• There are 24 coins in a brown paper bag.
  Determine how many nickels and how many dimes are
  in the bag if the total value of the bag is 1.60

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CE

• The total points that a basketball team scored
  was 96. If there were two-anda-half times as
  many field goals as free throws, how many of each
  were there.
• (Field goals count 2 pints free throws count 1
  point. There are no 3 point field goals. )

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Page 128

• 1 15 odd
• 34 48 even