Function Explicitly - 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: Function Explicitly, Inverse Function, Domain, Inverse, Partial Graph, Under Re°Ection, Remainder, Domain, Odd Function, Asymptotes

Typology: Exams

2012/2013

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Math 100 Second Midterm
Instructor: Dr. Sandy Rutherford
Date: November 12, 2004
Time: 11:30 12:20
Name (please print):
Signature:
Student Number:
Read the questions carefully, show all of your work and present organised solutions. If we do
not understand what you are doing, you will receive zero marks. You must give reasons for
your answers.
No calculators of any kind may be used. The use of any type of calculator is considered as
academic dishonesty.
No notes or textbooks may be used.
Some answers may contain radicals of the form 2. These should be simplified where possible;
however, a decimal expansion is not required.
If you require more room for your solutions, you may use the backs of the pages. However,
cross out any rough work that you do not wish to be graded.
This exam has 8 pages, including this cover page. Please be sure that you have all of the
pages.
Question Mark Total Marks
1 6
2 5
3 8
4 8
5 8
Total 35
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Math 100 — Second Midterm

Instructor: Dr. Sandy Rutherford

Date: November 12, 2004

Time: 11:30 – 12:

Name (please print):

Signature:

Student Number:

  • Read the questions carefully, show all of your work and present organised solutions. If we do

not understand what you are doing, you will receive zero marks. You must give reasons for

your answers.

  • No calculators of any kind may be used. The use of any type of calculator is considered as

academic dishonesty.

  • No notes or textbooks may be used.
  • Some answers may contain radicals of the form

2. These should be simplified where possible;

however, a decimal expansion is not required.

  • If you require more room for your solutions, you may use the backs of the pages. However,

cross out any rough work that you do not wish to be graded.

  • This exam has 8 pages, including this cover page. Please be sure that you have all of the

pages.

Question Mark Total Marks

Total 35

1. For the following functions, determine the inverse function. Be sure to state the domain of

the inverse function explicitly.

(a) f (x) = 2x + 3

(b) g(x) =

x

3. State the domain and range of each of the following functions. Also, calculate the y-intercept,

find any roots, find all asymptotes (horizontal, vertical, or slant), and state which functions

are even or odd under reflection about the y-axis. Finally, sketch a reasonably accurate graph

for each function.

(a) g(x) =

x

[Part (b) on next page.]

(b) f (x) =

x

3

+ x

x

2

(c) Find all values of x for which the composition p ◦ f satisfies (p ◦ f )(x) = 0.

5. We will a use a quadratic equation to model the blood alcohol concentration of a student

who has just drunk 3 bottles of beer. The student’s blood alcohol concentration, which was

initially 0%, returns to 0% after 4 hours. When was the maximum concentration reached?

Suppose that the student’s blood alcohol concentration was measured as 0.09% one hour after

drinking the beer. What was the maximum value of the blood alcohol concentration?