04faex01 - Math 171 Fall 2004 C. Gmez o October 5, 2004...

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Unformatted text preview: Math 171 Fall 2004 C. Gmez o October 5, 2004 Exam 1 Name: TA's Name Section Time Problem Score No calculators, notes, or books are allowed. You must show all your work, and explain your reasoning to receive credit for your answers. Be sure to check your answers whenever possible. Good luck! 1 2 3 4 5 Total Math 171 Exam 1 1. Solve the following equations. (a) [10 points] 7x + 2 + x = 6 2 (b) [10 points] 6x + 11 3x + 1 = 5x + 7 10x - 3 Math 171 Exam 1 3 2. [12 points] Find all real solutions of 10x2 +11x > 6. Express your answer in interval notation. Math 171 Exam 1 3. Sketch the graphs of the following equations and label the x- and y-intercepts. (a) [14 points] y = -x2 - 2x + 3 4 Math 171 Exam 1 3. (Continued) (x - 1)2 f (x) = 3x 6 if x < 0 if 0 x < 2 if x 2 5 (b) [14 points] Math 171 Exam 1 4. Let f (x) = x - 2 and g(x) = 1 . x+3 6 (a) [6 points] Find f g and express its domain in interval notation. (b) [6 points] Find g f and express its domain in interval notation. (c) [12 points] Verify that g f is one-to-one and find (g f )-1 . Math 171 Exam 1 7 5. In an effort to help slow down tuition hikes, the University of Wisconsin has decided to fence off a beach on Lake Mendota so they can charge admission. Funds have been allocated for 80 meters of fencing. The area to be enclosed will be a rectangle, but only three sides will require fencing--the fourth side of the rectangle will be the lake shore. (a) [8 points] Express the area of this rectangular beach as a function of the length of one of its sides. (b) [8 points] Using only the methods covered so far in this course, find the maximum area that can be enclosed in this way. ...
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04faex01 - Math 171 Fall 2004 C. Gmez o October 5, 2004...

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