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Lesson 2-7: Graphing Rational Functions

Lesson 2-7: Graphing Rational Functions. Advanced Math Topics Mrs. Mongold. Definitions. Continuity: a graph that is able to be traced without picking up the pencil Asymptote: a line that the graph of the function approaches, but never touches (this line is graphed as a dotted line)

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Lesson 2-7: Graphing Rational Functions

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  1. Lesson 2-7: Graphing Rational Functions Advanced Math Topics Mrs. Mongold

  2. Definitions • Continuity: a graph that is able to be traced without picking up the pencil • Asymptote: a line that the graph of the function approaches, but never touches (this line is graphed as a dotted line) • Point discontinuity: a hole in the graph

  3. Vertical Asymptote

  4. Horizontal Asymptote To Find A Horizontal asymptote look at the degrees of the numerator and denominator *If the degree of the denominator is greater than the degree of the numerator, then the horizontal asymptote is y=0 *If the degree of The denominator is equal to the degree of the numerator then the horizontal asymptote is found by dividing the coefficients of the leading terms. y=1, is the horizontal asymptote because the coefficients of the leading terms =1

  5. Point Discontinuity

  6. Steps to Graph a Rational Function • 1. Factor and simplify if you can • 2. Look for the vertical asymptote • 3. Look for the horizontal asymptote • 4. Draw asymptotes as dotted lines on your graph • 5. Find 2 x values so that one is greater than the vertical asymptote and one is less than the vertical asymptote ( If there is no vertical asymptote you must make an x-y chart and find at least 5 points to sketch the graph) • 6. Plot the two points and sketch the graph by stretching toward the asymptotes.

  7. Graphing Rational Functions

  8. Graphing Rational Functions

  9. Graphing Rational Functions

  10. Graphing Rational Functions

  11. Homework • Pg 124/ 12-18 Even

  12. Day #2 • Evaluate Rational Functions just like you would any other function. Finding f(4) simply means plug 4 in for x. • When you are looking for x and you know f(x) = some # then you replace the f(x) in function notation with the # you are given and solve for x

  13. Find f(4) and then find x when f(x) = 3

  14. Find g(t)=-3

  15. Word Problems • Roy took two tests and his average is 63. If he scores 100 on the rest of his tests, how many more tests does Roy need to take to raise his average to 85?

  16. Arlene realized while she was making plans for her children’s education that she was seven times as old as her youngest child, Mark, who is 5 years old. In how many years will Arlene be twice as old as Mark?

  17. Homework • Pg 124/ 2-9

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