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RATIONAL FUNCTIONS II GRAPHING RATIONAL FUNCTIONS.

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1 RATIONAL FUNCTIONS II GRAPHING RATIONAL FUNCTIONS

2 Steps to Graphing Rational Functions
Connect points and head towards asymptotes. Find some points on either side of each vertical asymptote Steps to Graphing Rational Functions Find horizontal or oblique asymptote by comparing degrees Test for symmetry by putting –x in for x. (remember even, odd test) Find the x intercepts if there are any by setting the numerator of the fraction = 0 and solving. Find the y intercept if there is one. Remember we find the y intercept by putting 0 in for x Find the domain. Excluded values are where your vertical asymptotes are.

3 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 Find the domain. Excluded values are where your vertical asymptotes are.

4 So let’s plot the y intercept which is (0, - 1)
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 So let’s plot the y intercept which is (0, - 1) Find the y intercept if there is one. Remember we find the y intercept by putting 0 in for x

5 But 0 = 6 is not true which means there IS NO x intercept.
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 If the numerator of a fraction = 0 then the whole fraction = 0 since 0 over anything = 0 But 0 = 6 is not true which means there IS NO x intercept. Find the x intercepts if there are any by setting the numerator of the fraction = 0 and solving.

6 Not the original and not negative of function so neither even nor odd.
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 Not the original and not negative of function so neither even nor odd. Test for symmetry by putting –x in for x. (remember even, odd test)

7 Find horizontal or oblique asymptote by comparing degrees
degree of the top = 0 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 remember x0 = 1 degree of the bottom = 2 If the degree of the top is less than the degree of the bottom the x axis is a horizontal asymptote. Find horizontal or oblique asymptote by comparing degrees

8 Choose an x on the right side of the vertical asymptote.
Choose an x on the left side of the vertical asymptote. 2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 x R(x) -4 0.4 1 -1 4 1 Choose an x in between the vertical asymptotes. Find some points on either side of each vertical asymptote

9 Pass through the point and head towards asymptotes
2 -7 -6 -5 -4 -3 -2 -1 1 5 7 3 4 6 8 There should be a piece of the graph on each side of the vertical asymptotes. Go to the function grapher or your calculator and see how we did. Pass through the points and head towards asymptotes. Can’t go up or it would cross the x axis and there are no x intercepts there. Connect points and head towards asymptotes.

10 Acknowledgement I wish to thank Shawna Haider from Salt Lake Community College, Utah USA for her hard work in creating this PowerPoint. Shawna has kindly given permission for this resource to be downloaded from and for it to be modified to suit the Western Australian Mathematics Curriculum. Stephen Corcoran Head of Mathematics St Stephen’s School – Carramar

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