393 3.5 Rational Functions: Graphs, Applications, and Models (c) What happens to the number of vehicles waiting as the traffic intensity approaches 1? SOLUTION (a) The average arrival rate is 2.6 vehicles per minute and the average admittance rate is 3.2 vehicles per minute, so x = 2.6 3.2 = 0.8125. (b) A calculator graph of ƒ is shown in Figure 58. ƒ10.81252 = x2 211 - x2 = 0.81252 211 - 0.81252 ≈1.76 vehicles −2 0 5 1 f(x) = x2 2(1 − x) Figure 58 CONCEPT PREVIEW Provide a short answer to each question. 1. What is the domain of the function ƒ1x2 = 1 x ? What is its range? 2. What is the domain of the function ƒ1x2 = 1 x2 ? What is its range? 3. What is the largest open interval of the domain over which the function ƒ1x2 = 1 x increases? decreases? is constant? 4. What is the largest open interval of the domain over which the function ƒ1x2 = 1 x2 increases? decreases? is constant? 5. What is the equation of the vertical asymptote of the graph of y = 1 x - 3 + 2? Of the horizontal asymptote? 6. What is the equation of the vertical asymptote of the graph of y = 1 1x + 222 - 4? Of the horizontal asymptote? 7. Is ƒ1x2 = 1 x2 an even or an odd function? What symmetry does its graph exhibit? 8. Is ƒ1x2 = 1 x an even or an odd function? What symmetry does its graph exhibit? 3.5 Exercises (c) From the graph, as x approaches 1, y = ƒ1x2 gets very large. Thus, the average number of waiting vehicles gets very large. This is what we would expect. S Now Try Exercise 113.
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