R(X)=6 ___ X^2-X-6 Please show all these steps so I can figure out how to do it!
ID: 3107194 • Letter: R
Question
R(X)=6___
X^2-X-6
Please show all these steps so I can figure out how to do it!!
1. Factor and the domain of the rational function.
2. Write in lowest terms.
3. Locate intercepts of the graph, determine behavior of the graph near each x-intercept. Then plot them and indicate the behavior of the graph near it.
4. Locate vertical asymptotes and graph.
5. Locate horizontal or oblique asymptote.
6.Use the zeros of the numerator and denominator of R to divide the x-axis into intervals. Determine if the graph of R is above or below x-axis
7. graph it
Explanation / Answer
1) You need to determine what all can be factored. The numerator is a constant, so it can't go any lower. However the denominator can be factored into the form (x+_)(x-_) 2) Once you have your factored expression, see if anything cancels out with the 6 in the numerator 3) for the intercepts, set the opposite variable equal to 0. Finding the x intercept you set R(x)=0 and solve for x... set x=0 to solve for R(x). To find the behavior near it, plug in values close to them 4) verticle asymptotes will be found most commonly at a divide by 0, so figure out where the denominator equals 0 5)horizontal asymptotes occur as the limit-> +/-infinity 6) Just as it says... group the graph into chunks based on where the zeros fall 7) plot points!
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