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Notes 8.2

Notes 8.2. Graph Simple Rational Functions. Rational Functions. Ratio of two polynomial functions f(x) = p(x)/q(x) , q(x) ≠ 0 Inverse Function is rational function f(x) = a/x. Inverse Function. Graph is a hyperbola Symmetrical parts Vertical and Horizontal Asymptotes

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Notes 8.2

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  1. Notes 8.2 Graph Simple Rational Functions

  2. Rational Functions • Ratio of two polynomial functions • f(x) = p(x)/q(x) , q(x) ≠ 0 • Inverse Function is rational function • f(x) = a/x

  3. Inverse Function • Graph is a hyperbola • Symmetrical parts • Vertical and Horizontal Asymptotes • Domain and Range: all nonzero real numbers (x ≠ 0, y ≠ 0)

  4. To graph simple rational functions: y = a/(x-h) + k Step 1) Sketch the asymptotes: x = h and y = k vertical horizontal Step 2) Use a basic table of values to plot 2-3 points on each side of the vertical asymptote (i.e. x = h-3, h-2, h-1,& h+1, h+2, h+3) (or multiples of a) Step 3) Sketch the two halves of the hyperbola. Step 4) Label the graph with the equation, and label all asymptotes.

  5. EX. y = a/x • Vertical Asymptote: y = 0 • Horizontal Asymptote: x = 0 • x = -2, -1, 1, 2

  6. EX. y = -3/(x + 2) -1 Asymptotes: x = -2, y = -1

  7. Graph and Label

  8. Your Turn • 561 (graphs = 3 parts) get 5pt • Level A: 3,5, 11,13, 27 • Level B: 8, 16,18, 31 • Level C:10 22, 34

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