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Math 111 Fall 2003 Second Midterm Examination Solutions, Exams of Algebra

The solutions to the math 111 fall 2003 second midterm examination. It includes true or false questions, multiple choice questions, open-answer questions, and an extra credit problem. Various topics in mathematics such as functions, logarithms, and algebra.

Typology: Exams

Pre 2010

Uploaded on 07/23/2009

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Second Midterm Examination
Math 111, Fall 2003, Chris Phan
Monday, 24 November 2003
Name:
Good luck! Be sure to do all the pages! (36 points total)
True or False. Circle “T” if the statement is always true. (Always!)
Otherwise, circle “F”. (2 points each, 12 points total)
1. T F If 3 is a root of the polynomial function then x+ 3
is a factor of the polynomial.
2. T F 4x+y2= 8 defines yas a function of x.
3. T F If fis an odd function and the point (2,3) is on
the graph of fthen the point (2,3) is on the graph of f.
4. T F The function f(x) = x
|x|+2x4is an odd function.
5. T F (fg)(x) = (gf)(x) for all functions f(x) and
g(x).
6. T F 3x9y= 3x+2yfor all xand y.
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Second Midterm Examination

Math 111, Fall 2003, Chris Phan

Monday, 24 November 2003

Name:

Good luck! Be sure to do all the pages! (36 points total) True or False. Circle “T” if the statement is always true. (Always!) Otherwise, circle “F”. (2 points each, 12 points total)

  1. T F If −3 is a root of the polynomial function then x + 3 is a factor of the polynomial.
  2. T F 4 x + y^2 = 8 defines y as a function of x.
  3. T F If f is an odd function and the point (2, −3) is on the graph of f then the point (− 2 , 3) is on the graph of f.
  4. T F The function f (x) = (^) |x|+2xx 4 is an odd function.
  5. T F (f ◦ g)(x) = (g ◦ f )(x) for all functions f (x) and g(x).
  6. T F 3 x 9 y^ = 3x+2y^ for all x and y.

Multiple Choice Write the letter corresponding to the correct answer in the space provided. (2 points each, 16 points total)

  1. The inverse of the function f (x) = (^) x^4 +1 is: a) f −^1 (x) = x+1 4 b) f −^1 (x) = 4+ xx c) f −^1 (x) = 1 − xx d) f −^1 (x) = 4 − xx
  2. A rectangular box (with top) has a square base. The sum of the lengths of its 12 edges is 8 feet. What dimensions should the box have so that its surface area is as large as possible? a) 12 ft. × 23 ft. × 1 ft. b) 23 ft. × 23 ft. × 23 ft. c) 1 ft. × 1 ft. × 1 ft. d) 32 ft. × 32 ft. × 32 ft.
  3. What is the smallest possible degree of the polynomial function f whose graph appears above? a) 4 b) 5 c) 6 d) 7

Open answer. Show all work. Answers may include “undefined” or “no solution”. (8 points total)

  1. Draw a complete graph for the rational function

f (x) = (^) x 2 x+^ − x^1 − 2.

Be sure to show any holes, asymptotes, or intercepts. (5 points)

  1. Solve |x^2 + 3x + 1 − ln(x^2 + 3x)| < −2. (3 points)

Extra credit. You must show all work to get credit. EC. (5 points) Find and simplify the difference quotient of f (x) = (x + 1)^2.