Today%20in%20Pre-Calculus

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Today in Pre-Calculus

• Turn in info sheets
• Need a calculator (can share, if you borrow one,
  leave something in the basket)
• Define and Identify a function
• Define and find the Domain of a function
• Define and find the Range of a function
• Homework

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Functions

• Definition A function from a set D to a set R is
  a rule that assigns to every element in D a
  unique element in R.
• Familiar Definition For every input (x) there is
  only one output (y).
• x The independent variable
• y The dependent variable

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Functions

• To be a function a graph must pass the vertical
  line test which states a graph (set of points
  (x,y)) in the xy-plane defines y as a function of
  x iff no vertical line intersects the graph in
  more than one point.

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Functions

• Which of the following are functions?
• a. b.
• c. d.

Function
Not
Not
Function
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Domain and Range

• Definitions Given a function , the DOMAIN of the
  function is the set of all permissible inputs and
  the RANGE is the set of all resulting outputs.
• Domains can be found algebraically ranges are
  found algebraically or graphically. Domains and
  Ranges are sets. Therefore, you must use the
  proper notation.

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Domain and Range

• Proper Notation
• set (of intervals)
• , interval includes the endpoints
• ( , ) interval does not include the
  endpoints
• - the union (of intervals)

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Finding the Domain

• For polynomials the domain is the set of all real
  numbers R.
• Square root functions can not be negative, so set
  the expression under the radical 0 and solve.
  This will be your domain.
• Rational functions can not have zero in the
  denominator. Set the denominator ? 0. This will
  be the exclusion from the domain.

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Find the Domain

• Determine the domain for the following functions
• 1.
• Domain ___________
• 2.
• Domain _____________
• 3.
• Domain _____________

R or (8, 8)
(8, 2/3
(8 , 2) U (2, 2) U (2, 8)
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Find the Range

• With the aid of a graphing calculator find the
  range of
• Domain
• No zero in denom.
• Range
• It also appears zero is not in the range.
  (Function itself can never equal zero since the
  numerator is a constant). Remember, you are
  interested in the vertical span of the graph.

(-8,0) (0,8)
(-8,0) (0,8)
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Practice Find the Domain
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Homework

• Worksheet