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Simon Fraser University
Math 100
Midterm 2- Exam 1 Date: March 5, 2008
Time: 11:30 - 12:
Last Name (print): First Name
Signature: SFU Email ID:
Instructions:
- Do not open this exam until instructed to do so.
- No calculators, notes or books are allowed.
- When presenting a final answer for your solution, calculator-ready expressions will be given full credit.
- Show all your work. No credit will be given for an answer without the correct explanation and accompanying work.
- Answer the questions in the space provided. Continue on the back of the pre- vious page if necessary.
Question Mark Maximum
Total 44
- Decide if the following statements are true or false. In each case mark (circle or cross) the correct answer. Show all work and/or give a reason for your decision. NO credit will be given for an answer without explanation or supporting work.
[1 pts] (a) According to the rational zeroes theorem the number x = โ 1 /2 is a can- didate for a zero of the polynomial x^3 โ 6 x^2 + 5x โ 6. [TRUE] [FALSE]
[1 pts] (b) The graph of a rational function can have more than one horizontal asymp- tote. [TRUE] [FALSE]
(c) According to the intermediate value theorem if f (x) = x^3 โ 6 x^2 + 2 then [1 pts] there is a value 0 < c < 1 for which f (c) = 0.
[TRUE] [FALSE]
- Let f (x) = โ 4 x^3 + 24x^2 โ 36 x, answer the following questions about f (x):
[2 pts] (a) Describe the end behavior of f (x) (you can use a picture).
[2 pts] (b) Determine if f is even, odd or neither. Explain
[3 pts] (c) Find the x and y-intercepts of the graph of f (x).
- Given the rational function h(x) = (4x^ + 8)(x
(^2) + 2x + 1) (x^2 โ 4)(3x + 9)
answer the following questions about h.
[6 pts] (a) Determine if the graph of h has any holes or asymptotes. If so, give the equation of the asymptotes and state the location of the holes.
[4 pts] (b) Give the x and y-intercepts.
[2 pts] (c) State the domain of h(x).
- Let f (x) = โ2 sin(3x + 4).
[2 pts] (a) Find the amplitude of f.
[2 pts] (b) Give the phase-shift of f.
[2 pts] (c) State the period of f.
[2 pts] (d) Choose, from the following, the graph of f. Clearly indicate your choice.
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