Step 1: Find the y-intercept by letting x=0.
Step 2: Factor everything, which in this case it's already factored.
Step 3: Find the roots of the function by finding the roots of the numerator.
This one has NO ROOTS.
Step 4: Find the vertical asymptotes by finding the roots of the denominator.
V.A. → x=2
Step 5: Find the horizontal asymptotes by dividing each term in the function by highest power of x, and take the limit as x goes infinity.
H.A. → y=0
Step 6: Determine the sign of the function over the intervals defined by the roots (step 3) and vertical asymptotes (step 4).
Step 7: Sketch the graph.
This is not the the exact graph, but it gives us idea on how the graph would look like.
We did another example on graphing rational functions, but it's pretty much the exact same thing on how we solve it. The only thing that changed was the graph (we can see this on the slides that Mr. K post everyday).
Homework: Go back to the Exercise that was assigned yesterday and and do the graphing rational functions part of it. Also, don't forget to start on doing the last exercise in the book that covers all the units that we did in Pre-Cal.
Next scribe is Larlyn