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quiz2-10.40-soln. - y&& 4 the y-intercept and y& 2...

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MATH 101-B Fall 2004 Quiz 2 ( 10:40-12:30 Group) Oct. 08, 2004 Time: 15 minutes Name: Student No: Follow the directions. No work ° No credit!! Problem 1 (7 pts.) The graph of y ° f ° x ± is shown in the figure. Sketch the graph of y ° ° 2 f ° x /2 ± ° 1. Label any intercepts or asymptotes that can be determined. 5 4 3 2 1 0 -1 -2 -3 -4 -5 2 1.5 1 0.5 0 -0.5 -1 -1.5 -2 x y f ° x ± Solution. The following sequence of changes need to be made on the above graph: Stretch x -axis by a factor of 2; stretch vertically by a factor of 2; flip around the x -axis; shift everything down by 1. In the original graph, y ° ° 2 is the y -intercept and y ° 1 is a horizantal asymptote. The first step doubles x -intercepts, which are in the intervals ° ° 2, ° 1 ± and ° 1,2 ± . The second step makes
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Unformatted text preview: y & & 4 the y-intercept and y & 2 the horizantal asymptote. Third step changes the signs of y-intercept and horizantal asymptote. The last step makes y & 3 the y-intercept and y & & 3 the horizantal asymptote. It also affects the x-intercepts. The resulting graph is: 6 4 2-2-4-6 3 2 1-1-2-3 x y & 2 f & x /2 ± & 1 Problem 2 (3 pts.) Prove the identity: log a b & ln b ln a Solution. Let’s say log a b & x . We want to show that x & ln b ln a . Follow the steps below: a x & b rewriting log. as exponential ln a x & ln b taking ln of both sides x ln a & ln b use a property of logarithms x & ln b ln a ....
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