The problem shows you how to graph a rational function when the degree is bigger on top and one bigger than the bottom degree, meaning that it has no horizontal asymptote and it has a slant asymptote. In this problem, you perform long division in order to get your slant asymptote equation in slope-intercept form that gives you your first two points for the graph. Cross off any common factors from your factored equation and your remaining factor's zero is your VA equation. Plot any holes from the equation, any crossed off common factors equal to zero then for your y-value you must plug in your x-value into the simplified equation, not the factored. We found the domain of the equation: the x-value of my vertical asymptote. The x-intercepts are found by plugging zero for y using the factored equation, canceling the denominator, then setting the numerator's factors equal to zero. For the y-intercept plugging in 0 for all of the x's and solving factor the numerator and denominator of the function Be sure to graph all of the pieces on the graph: sketch asymptotes (slant/vertical), plot any holes, plot x-intercept and y-intercept and tracing any other needed points for the graph.
Pay attention when factoring your numerator and denominator, making sure it's not incorrect otherwise you will not graph the rational function right. Remember that we do not include our remainder from long division into our slant asymptote equation, you must plug in the x-value into the simplified equation to get the y-value meaning you do not use your factored equation. Make sure you put parenthesis around your correct rational function when inputting in your calculator tracing to get other values. Be sure to sketch your graph correctly, not to cross through the vertical asymptote.
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