110quiz5solutions

# 110quiz5solutions - Math 110 Quiz 5 Oct. 19, 2006 2 Name: x...

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Math 110 Quiz 5 Oct. 19, 2006 Name: 1) Let R ( x ) = x 2 - 5 x 2 +4 x , a rational function. (a) Determine the x and y intercepts of R ( x ). (b) Give the equations of any vertical asymptotes. (c) Give the equations of any horizontal asymptotes. (d) Sketch a graph of R ( x ), plotting additional points if necessary. Be sure that your graph indicates inter- cepts and asymptotes. Solutions: (a) To ﬁnd x -intercepts we solve R ( x ) = 0, in other words x 2 - 5 = 0. This gives x = ± 5, so the x -intercepts are ( ± 5 , 0) To ﬁnd the y -intercept we ﬁnd R (0). R (0) = - 5 0 , which is undeﬁned. Hence there are no y -intercepts. In fact, the y -axis is a vertical asymptote as we’ll see below. (b) To ﬁnd vertical asymptotes, we solve x 2 + 4 x = x ( x + 4) = 0. Hence x = 0 and x = - 4 are ver- tical asymptotes. (c) To ﬁnd horizontal asymptotes, we compare the degrees of the numerator and denominator. Since they are both quadratic, we have a horizontal asymptote at the ratio of the leading coeﬃcients: y = 1 (d) 1

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2. The population of the world doubles roughly every 38 years. In 1995, the world population was 5.8
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## 110quiz5solutions - Math 110 Quiz 5 Oct. 19, 2006 2 Name: x...

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