Evaluating and Graphing Polynomial Functions

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Evaluating and Graphing Polynomial Functions

• Chapter 6.2

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Vocabulary
degree

• Polynomial funtion
• Do not let the notation confuse
• you! Simply put, the an terms
• are the coefficients and the xn
• terms are the powers.
• Standard Form Put the polynomial in order from
  the highest power (degree) to the constant term
• Example

Leading coefficient
constant
3
Types of polynomial functions
4
Examples

• Determine whether the function is a polynomial
  function.
• Yes. It is a 4th degree polynomial.
• No. The power of 3 is not a number,
  it is a variable.

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End Behavior of a function

• The end behavior of a function the graphs
  behavior as x approaches -? and ?. In other
  words, what happens to the values of f(x) as x??
  and -?.
• Ex In the graph, as x???, the
  values of f(x) get larger, and thus
  f(x)???.

Special Notation ? is read approaches
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More on End Behavior
Describe the end behaviors of f(x) and g(x).
For f(x) f(x) ? ?? as x ? ?? and f(x) ? ?
as x ? ? For g(x) g(x) ? ? as x ? ?? and
g(x) ? ? as x ? ?

• End Behavior Summary
• If the polynomial is even, the graph opens up (or
  down if the leading coefficient is negative) and
  the end behaviors at ???? are the same.
• If the polynomial is odd, the graph opens in
  opposite directions (both up and down) and the
  end behaviors are reversed (one of end the graph
  will approach ?? and on will approach ??)

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Graphs of Polynomial Functions
End behavior End behavior