Integer Function - PreCalculus - Exam, Exams of Calculus

This is the Exam of PreCalculus which includes Irrational Number, Decimal Expansion, Rational, Equations, Polynomials, Prime, Factored, Integer Coe±Cients, Explicit Factorisation etc. Key important points are: Integer Function, Function, Greatest, Two Functions, Domains, Identity Function, One to One, Domain, Complete Factorization, Zeros

Typology: Exams

2012/2013

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MATH 100-D200 Instructor: R. Pyke
Midterm 2, November 9, 2007
Last Name:
First Name:
SFU Student email : @sfu.ca
1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.
2. Clearly explain your answer. No credit will be given for just
writing down the answer.
3. If the answer space provided is not sufficient, write your answer
on the back of the previous page.
4. Ordinary Scientific Calculators ONLY are allowed.
NO GRAPHING CALCULATORS ALLOWED.
5. Copying someone else’s test, or deliberately exposing written
papers to the view of others is forbidden and will result in a
score of zero and disciplinary action.
Question Score Max
1 9
2 8
3 7
4 5
5 6
6 4
7 10
8 3
9 4
Total 57
Page 1 of 7
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MATH 100-D200 Instructor: R. Pyke

Midterm 2, November 9, 2007

Last Name:

First Name:

SFU Student email : @sfu.ca

1. DO NOT LIFT UP THE COVER PAGE UNTIL INSTRUCTED.

2. Clearly explain your answer. No credit will be given for just

writing down the answer.

3. If the answer space provided is not sufficient, write your answer

on the back of the previous page.

4. Ordinary Scientific Calculators ONLY are allowed.

NO GRAPHING CALCULATORS ALLOWED.

5. Copying someone else’s test, or deliberately exposing written

papers to the view of others is forbidden and will result in a

score of zero and disciplinary action.

Question Score Max 1 9 2 8 3 7 4 5 5 6 6 4 7 10 8 3 9 4 Total 57

(1) [Marks: 9] Sketch the graph of the function f (x). Remember that bxc denotes the greatest integer function.

f (x) =

   

bx − 1 c x < 0

|x^2 − 4 x + 3| 0 ≤ x ≤ 5

| 3 x − 18 | 5 < x

(3) [Marks: 7] Find two functions f, g, neither of which is the identity function I(x) = x, such that F = f ◦ g where F (x) = x + 3 − √x + 3 + 1^2 + 1

(4) [Marks: 5] (a) Prove that f (x) = (^) xx^ + 1− 1 is one-to-one.

(b) Prove that g(x) = x x 22 + 1− 1 is not one-to-one.

(5) [Marks: 6] Find f −^1 (x) for the function f (x) = x^2 − 4 x + 3 with domain (−∞, 2]

(6) [Marks:4] 5 is a zero of f (x) = 4x^3 − 20 x^2 − x + 5. Find all the other zeros and give the complete factorization of f (x).

(8) [Marks: 3] Find all the roots (including complex roots) of p(x) = x^3 + 2x^2 + 3x.

(9) [Marks: 4] Find the partial fraction decomposition of g(x) = (^) x(x − 2)(2^1 x − 1).