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Rational, Irrational & Absolute Value Functions Review
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Rational, Irrational & Absolute Value Functions Review

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Transcript

  • 1. Unit 3 Review Rational Functions, Irrational Functions, Absolute Value Functions
  • 2. Graphing Rational Functions
    • Consider the following function:
    • Find…
    • x-intercept(s)
    • y-intercept
    • Point(s) of discontinuity
    • Vertical Asymptote(s)
    • Horizontal Asymptote
    • Oblique Asymptote
    • Then sketch the graph
  • 3. Graphing Rational Functions
    • Consider the following function:
    • Find…
    • x-intercept(s) 2. y-intercept
    • 3. Point(s) of discontinuity
    • Vertical Asymptote(s) x= - 1
  • 4. Graphing Rational Functions
    • Consider the following function:
    • Find…
    • Horizontal Asymptote
    • Oblique Asymptote – can use simplified form of equation (factored).
    • Then sketch the graph!
  • 5. Graphing Rational Functions
    • Graph using your information.
    • Points: (0,0), (3,0); POD @ x=-3; VA @ x=-1; OA @ y=x-4
  • 6. Graphing Absolute Value Functions
      • If the function is linear, we can evaluate these as transformations that have been applied to y = |x|.
      • Ex: Sketch the graph of y = -2|x-5|
      • What transformations are there?
      • Horizontal translation +5
      • Stretch of 2
      • Reflection across the x-axis
      • If the function is non-linear – then simply graph the original and ‘flip’ the negative parts (like we did in class).
  • 7. Solving, Simplifying…
    • When simplifying a rational expression that is being multiplied or divided, factor first, simplify, then multiply top with top, bottom with bottom & state restrictions: no zeros in the denominator!
    • Ex: Simplify the following expression, stating any restrictions.
  • 8. Solving, Simplifying…
    • When simplifying a rational expression that is being added or subtracted, you need each expression to have the same denominator.
    • Ex. Solve for b.
  • 9. Inequalities
    • When solving inequalities – remember the goal is to either isolate x, or set one side to zero. Simplify as much as you can. Either draw a graph or use the number line method – show your work, including test value(s).
    • Ex. Solve the following inequality.
    • Zeros from numerator:
    • Zeros from denominator: