PROBLEM 3. Sketch the graph of y = . Plot all extrema, points of inflection, and asymptotes.
Answer: This should seem rather routine by now.
Find the x-intercepts by setting the numerator equal to zero; x = 4. The graph has an x-intercept at (4, 0).
(It’s a double root.)
Next, find the y-intercept by plugging in x = 0.
y = The denominator is undefined at x = −3, so there’s a vertical asymptote at that point.
Look at the limits.
= 1 and = 1The curve has a horizontal asymptote at y = 1.
It’s time for the first derivative.