Unformatted text preview: y 012 (part 1 of 1) 10 points Which of the following is the graph of f (x) = 1 -x x2 6. 13 5. when dashed lines indicate asymptotes? 1. 7. 2. correct 8. 3. Explanation: Note first that the vertical asymptote must be the y-axis. On the other hand, since 4.
x lim f (x) + x = lim x 1 = 0, x2 the line y = x is a slant asymptote. This already eliminates four of the eight possible graphs. To identify which of the remaining four graphs is that of f we can use concavity because each graph is always concave up or Garcia, Ilse Homework 11 Due: Nov 6 2007, 3:00 am Inst: Fonken always concave down, on either side of the y-axis. Now f (x) = - in which case f (x) > 0 on (-, 0) , while f (x) > 0 on (0, ) . Thus the graph of f is concave up both to the left and right of the y-axis. Consequently, the graph of f is 2 - 1, x3 f (x) = 6 , x4 14 keywords: graph, vertical asymptote, rational function, slant aymptote, concavity,...
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This note was uploaded on 01/16/2009 for the course M 408k taught by Professor Schultz during the Spring '08 term at University of Texas.
- Spring '08
- Differential Calculus