In this video we discuss how to get all needed plots in order to graph a rational function. First, we need a rational function equation and a rational function equation must be a fraction with both the numerator and the denominator being polynomials. Then we decide whether our equation has a horizontal asymptote or a slant because a function can NEVER have both. If we refer to our in-class-chant we know that if the degree on Top is One bigger than the degree on bottom, we have a slant! And to get that slant equation, we need to use long division but ignore the reminder. Next is to find vertical asymptotes and holes. If after factoring both the top and the bottom we notice that a set in parenthesis can be canceled from top and bottom, then that becomes our hole(s) and we can now use the "simple" equation to set the denominator to zero and get our vertical asymptotes. Rememeber, Domain is always the vertical asymptotes and the holes (only x-intercept). To get the x and y intercepts, the simple equation must always be used. For x, set the numerator equal to zero; for the y, plug in 0 for every x value. After getting all of that, we must find three different plots for each side and only then may we solve. Check your graphing to get your plot ordered pairs.
The trickiest part in solving this equation was actually figuring out how to graph it. When plugging into my graphing calculator, it wouldn't give me an accurate graph and I didn't know why until I remembered that *parenthesis must always be put seperately around both the numerator and the denominator. After that it was then easy to solve.
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