Rational, Irrational & Absolute Value Functions Review

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Rational, Irrational & Absolute Value Functions Review

  1. 1. Unit 3 Review Rational Functions, Irrational Functions, Absolute Value Functions
  2. 2. Graphing Rational Functions <ul><li>Consider the following function: </li></ul><ul><li>Find… </li></ul><ul><li>x-intercept(s) </li></ul><ul><li>y-intercept </li></ul><ul><li>Point(s) of discontinuity </li></ul><ul><li>Vertical Asymptote(s) </li></ul><ul><li>Horizontal Asymptote </li></ul><ul><li>Oblique Asymptote </li></ul><ul><li>Then sketch the graph </li></ul>
  3. 3. Graphing Rational Functions <ul><li>Consider the following function: </li></ul><ul><li>Find… </li></ul><ul><li>x-intercept(s) 2. y-intercept </li></ul><ul><li>3. Point(s) of discontinuity </li></ul><ul><li>Vertical Asymptote(s) x= - 1 </li></ul>
  4. 4. Graphing Rational Functions <ul><li>Consider the following function: </li></ul><ul><li>Find… </li></ul><ul><li>Horizontal Asymptote </li></ul><ul><li>Oblique Asymptote – can use simplified form of equation (factored). </li></ul><ul><li>Then sketch the graph! </li></ul>
  5. 5. Graphing Rational Functions <ul><li>Graph using your information. </li></ul><ul><li>Points: (0,0), (3,0); POD @ x=-3; VA @ x=-1; OA @ y=x-4 </li></ul>
  6. 6. Graphing Absolute Value Functions <ul><ul><li>If the function is linear, we can evaluate these as transformations that have been applied to y = |x|. </li></ul></ul><ul><ul><li>Ex: Sketch the graph of y = -2|x-5| </li></ul></ul><ul><ul><li>What transformations are there? </li></ul></ul><ul><ul><li>Horizontal translation +5 </li></ul></ul><ul><ul><li>Stretch of 2 </li></ul></ul><ul><ul><li>Reflection across the x-axis </li></ul></ul><ul><ul><li>If the function is non-linear – then simply graph the original and ‘flip’ the negative parts (like we did in class). </li></ul></ul>
  7. 7. Solving, Simplifying… <ul><li>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! </li></ul><ul><li>Ex: Simplify the following expression, stating any restrictions. </li></ul>
  8. 8. Solving, Simplifying… <ul><li>When simplifying a rational expression that is being added or subtracted, you need each expression to have the same denominator. </li></ul><ul><li>Ex. Solve for b. </li></ul>
  9. 9. Inequalities <ul><li>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). </li></ul><ul><li>Ex. Solve the following inequality. </li></ul><ul><li>Zeros from numerator: </li></ul><ul><li>Zeros from denominator: </li></ul>

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