RATIONAL FUNCTIONS II GRAPHING RATIONAL FUNCTIONS St Ra

St Ra e tio ps na to l F Gr un ap ct hin

$If the numerator of a fraction = 0 then the whole fraction = 0$

degree of the top = 0 remember x 0 = 1 degree of the

Choose an x on the left side of the vertical asymptote. x -4 1

Pass through the point and head towards asymptotes There should be a piece of

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RATIONAL FUNCTIONS II GRAPHING RATIONAL FUNCTIONS

St Ra e tio ps na to l F Gr un ap ct hin io g ns Connect points and head towards asymptotes. Find some points on either side of each vertical asymptote 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 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.

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 Find the domain. Excluded values are where your vertical asymptotes are.

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 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

$If the numerator of a fraction = 0 then the whole fraction = 0$

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

-7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 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)

degree of the top = 0 remember x 0 = 1 degree of the bottom = 2 -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 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

Choose an x on the left side of the vertical asymptote. x -4 1 4 R(x) 0. 4 -1 1 Find some points on either side of each vertical asymptote Choose an x on the right side of the vertical asymptote. -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 Choose an x in between the vertical asymptotes.

Pass through the point and head towards asymptotes 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. Connect points and head towards asymptotes. Pass through the point and head towards asymptotes -7 -6 -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 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.