Difference Quotient

1
Difference Quotient

• An expression of the form

2
Evaluate the difference quotient

• f(x) x2 - 3x

3
Rational Functions

• General form is f(x) p(x)/q(x), where p(x) and
  q(x) are polynomial functions and
• q(x) ?0.
• Domain and range are restricted (denominators may
  not equal zero.)
• Basic graph is a hyperbola
• Graphs of rational functions may have boundary
  lines called asymptotes

4
Draw the graph and identify the asymptotes

• F(x) 1/x
• F(x) 1/x 2
• F(x) 1/(x - 2)
• F(x) 3x/(x 2)
• F(x) 3x/(x2 4)
• F(x) 3x2/(x2 4)
• F(x) 3/(x2 4)

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Asymptotes

• Vertical asymptotes occur at x c, where the
  domain is undefined.
• Horizontal asymptotes depend on the degrees of
  the numerator and denominator.
• Same degree HA is ratio of leading
  coefficients.
• Denominator has higher degree
• HA is y 0

6
Regression

• A mathematical tool used to find a function that
  best models a set of data.

7
Find the best model
8
Find the best model