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Math 1050 Final Exam Form E - Fall Semester 2007
Name: ________________________________ Instructor: __________________________
Student ID: ____________________ ID Verification: ____________ Section Number:____________
This exam has three parts: Part I โ Ten multiple choice questions Part II โ Ten open ended questions โ You MUST show all your work Part III โ Choose FIVE out of ten open ended questions โ You MUST show your work and indicate which five problems are to be graded
Students are NOT allowed to use books or notes.
Questions 1 โ 10 Multiple Choice. Answer all TEN questions and circle the correct answer.
- For f ( ) x = x^2 โ 1 , find
f ( x h ) f ( ) x h
; simplify your answer.
A) x + 2 h
B) 2 x + h
C)
2 xh h^22 h
D) 2 x โ 2 h
- Consider the demand equation 1 30; 0 450 15
p = โ x + โค x โค
where p represents the price and x the number of units sold. What price should the company charge to maximize the revenue? [Hint: Remember that Revenue = (quantity sold) โ
(price).]
A) $
B) $
C) $
D) $
- The sequence is defined recursively. What is the fourth term of this sequence?
a 1 = โ2, a 2 = 5 and a n = 3a n โ 1 + a n โ 2 for n โฅ 3
A) 135
B) 44
C) 27
D) 8
- Find the oblique asymptotes, if any, of the graph of
3 2 2
x x x f x x
A) y = 2 x
B) y = 2 x โ 3
C) y = 2 x + 7
D) No oblique asymptotes
- Form a polynomial f(x) with real coefficients having the given degree and zeros.
Degree: 3; zeros: 3 and -2 i
A) f ( ) x = x^3^ โ 3 x^2 โ 4 x + 12
B) f ( ) x = x^3 โ 3 x^2 + 4 x โ 12
C) f ( ) x = x^3 + 3 x^2 + 4 x + 12
D) f ( ) x = x^3^ + 4 x^2 โ 4 x โ 12
- The graph of an exponential function is shown ( a > 1 ). Select the function which matches the graph.
A) ( )^2
f x = โ a x +
B) ( )^2
x
f x a
โ
C)
( 2)
x
f x a
โ
D)
( 2)
x
f x a
โ
- The half-life of radioactive iodine is 8 days. If 20 grams are present now, how much will be present in 13 days? Round your answer to three decimal places. The decay follows the law of uninhibited radioactive decay.
A) 12.308 grams
B) 6.484 grams
C) 5.651 grams
D) 1.363 grams
- Solve the inequality. x^4 < 9 x^2
A) ( 3, 0)โ โช(0,3)
B) ( 3, 0)โ โช (3, โ)
C) ( โโ โ, 3) โช(0,3)
D) ( โโ โ, 3) โช (3, โ)
- Find the sum.
1
1
k
k
โ^ โ
=
A) 3
B) 5
C)
D) 15
Part II: Questions 11 โ 20, Open ended Answer all TEN questions. You must show your work in a clear and logical progression and clearly indicate your answer to receive full credit.
- The graph of a function f is illustrated. Use the graph of f as a first step toward graphing the following function. Label the x- and y-coordinates of the points corresponding to the labeled points of f(x). f(x) H ( x ) = f(x - 1 ) - 3
13)The function f is one-to-one. Find its inverse. State the domain and range of f and f โ^1.
x f x x
Domain of f : ____________________ Domain of f โ^1 : _____________________
Range of f : ____________________ Range of f โ^1 : _____________________
- Solve the equation.
log 3 x + log ( 3 x โ 8) = 2
- For the polynomial f ( ) x = x x ( + 3) (^2 x โ2)^3
a) Find the zeros of f ( ) x and their multiplicities and determine whether the graph of f ( ) x crosses or touches the x-axis at each zero.
Zero Multiplicity Touch/Cross
b) Find the power function that the graph of f ( ) x resembles for large values of x. (This is the end behavior.)
c) Sketch the function. Label all intercepts:
- Find the following sum. Assume the terms are from an arithmetic sequence.
โ1 + 3 + 7 + โฆ+ 195
- Graph f^ ( ) x^^ =^ log ( 2 x +^ 4) and find any intercepts. Determine the domain, range, and
vertical asymptote of f.
Domain:________________________
Range:_________________________
Vertical asymptote:_______________
x -intercept(s):________________
y -intercept:__________________
- Find the vertex and focus of the parabola. Show your work.
y^2 โ 6 y = x Vertex _________
Focus _________
Part III: Questions 21 โ 30, Self select
Choose FIVE out of the next TEN questions to complete. You must show all your work and clearly indicate your answer for full credit. CROSS OUT the problems that you do not want graded.
- Find the real solutions of the equation. 2 1
x^3 + 7 x^3 + 12 = 0
- Find the domain of ( ) 3
x f x x
- Use the following matrices to compute the given expression. Show your work.
A
= โข^ โฅ
B
, I (^) 2 is the 2 x 2 Identity matrix
BA + 2 I 2
- Let
2 2
x x f x x x
a) Find the domain of f.
b) Find the equations of the vertical asymptotes, if any, of the graph of f.
c) Find the x- and y- intercepts, if any, of the graph of f. (Express your answers as ordered pairs. That is, give both the x and y coordinates of the points.)
x-intercept(s):_________________
y-intercept:_________________
d) Find the equations of any horizontal or oblique asymptotes of the graph of f.
e) Graph the rational function f.
- Find the inverse of the following matrix. Use row operations and show your work.
A =
A โ^1 =________________
- Write the partial fraction decomposition of the rational expression. Solve for the constants (A, B, etc.).
5 13 ( 1)( 5)
x x x
