MATH 2233 Quiz: MATH 2233 OK State Quiz10 sol
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Since the denominator is zero when x + 2 = 0 or x 3 = 0, we must exclude 2 and 3 from the domain. 6 , so the y-intercept is at (0, 1. The numerator (2x + 1)(x + 2) is zero when x = 1. 2 or x = 2; the latter zero of the numerator is outside the domain of the function, so it is not a zero of the function as a whole. Thus, our only x-intercept is at ( 1. 2 , 0). (d) (4 points) find the horizontal, vertical, and slant asymptotes of this function. For each asymptote you identify, indicate which type it is, and give its equation. If the function has no asymptotes, explicitly say so. The function resembles 2x2 x3 = 2 x in the long term; as x becomes very large in magnitude, this dwindles to zero, so there is a horizontal asymptote at y = 0.
