Chapter 9 Rational Functions Inverse Variation Graphing Inverse

$Denominator CANNOT be 0! Since we are dealing with fractions, our denominators can never$

Brain Break https: //www. youtube. com/watch? v=Cbp. Ig. MJQERw

Real Life Example https: //prezi. com/axqjx 0 rhwx_s/application-of-functions-in-the-real-world/

More Complex Functions Sometimes there will not be linear functions in the denominator of

Points of Discontinuity Points of discontinuity are the breaks in a graph (asymptotes and

Finding Points of Discontinuity You find these points by setting the denominator equal to

Vertical Asymptotes vs. Holes The points of discontinuity will either be a vertical asymptote

Horizontal Asymptotes The graph of a rational function has AT MOST one horizontal asymptote.

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Chapter 9: Rational Functions

Inverse Variation

Graphing Inverse Variations

$Denominator CANNOT be 0! Since we are dealing with fractions, our denominators can never$

Denominator CANNOT be 0! Since we are dealing with fractions, our denominators can never be 0. Where ever the denominator would be 0, there will be an ASYMPTOTE on the graph. Asymptotes are imaginary lines that graphs will approach, but never cross.

Brain Break https: //www. youtube. com/watch? v=Cbp. Ig. MJQERw

Graph the Inverse Variation

Graphing with Translations

Warm-Up

Real Life Example https: //prezi. com/axqjx 0 rhwx_s/application-of-functions-in-the-real-world/

One More

More Complex Functions Sometimes there will not be linear functions in the denominator of the rational function. Therefore, we have to use our previous knowledge to solve for when denominator would equal 0.

Points of Discontinuity Points of discontinuity are the breaks in a graph (asymptotes and holes). (If you were to trace a continuous graph, you would never have to lift up the pencil, however you would have to if it was discontinuous. ) MOST rational functions will have an asymptote or a hole, however there are some that are continuous.

Finding Points of Discontinuity You find these points by setting the denominator equal to 0 and solve. If you get a real solution, it means at that x-value, the denominator will be zero. Since the denominator can never be 0, there will be a point of discontinuity there.

What are the Points of Discontinuity?

Warm-Up

Homework Answers

Algebra Refresher

Vertical Asymptotes vs. Holes The points of discontinuity will either be a vertical asymptote or a hole. When you factor: If nothing cancels out with numerator, your points of discontinuity will be vertical asymptotes. If something cancels out, then there will be a hole at that point.

Identify Asymptotes and/or Holes

Horizontal Asymptotes The graph of a rational function has AT MOST one horizontal asymptote. Will have a HA at y=0 if the degree of the numerator is LESS THAN the degree of the denominator. If the degree of the numerator and the denominator are equal, then the HA will be at y= ratio of the leading coefficients.

Identify the Horizontal Asymptote

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