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Material Type: Exam; Class: COLLEGE ALGEBRA; Subject: Mathematics; University: Idaho State University; Term: Fall 2007;
Typology: Exams
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Math 143: College Algebra Name:
Sample Final Exam Instructor:
Fall 2007 Section:
You are allowed to use a couple of 3 ร 5 cards of notes. Calculators are allowed.
Part I consists of 10 multiple choice questions worth 5 points each. Record your answers by placing an X through one letter for each problem on this answer sheet.
Part II consists of 10 partial credit problems worth a total of 100 points. Show all your work on the page on which the question appears.
Do not remove this answer page โ you need to return the whole exam. You are allowed two hours to do the exam. You may leave earlier if you are finished.
Answer Sheet
For Grading Use Only
1โ10 11 12 13 14 15
16 17 18 19 20 Total
Part I: Multiple Choice Questions
1 (5 points). Find the domain of the function y =
x^2 โ 1
(a) (โโ, โ1] โช [1, โ) (b) [โ 1 , 1] (c) (โโ, โ1) โช (1, โ) (d) (โ 1 , 1) (e) (1, โ)
2 (5 points). Determine which graph represents a one-to-one function.
x
y
x
y
x
y
(a) (b) (c)
x
y
x
y
(d) (e)
3 (5 points). Find the inverse function of f (x) =
2 x โ 1 x โ 3
(a) f โ^1 (x) =
x โ 3 2 x โ 1
(b) f โ^1 (x) =
1 โ 2 x x โ 3
(c) f โ^1 (x) =
2 x + 1 x + 3
(d) f โ^1 (x) =
3 x โ 1 x โ 2
(e) f โ^1 (x) =
x โ 2 3 x โ 1
7 (5 points). Find the vertical asymptote to the graph of the function y =
2 x โ 6 4 x + 8
(a) x = โ 2 (b) x = 12 (c) x = 2 (d) x = โ^34 (e) x = 3
8 (5 points). Find the solution set of the inequality ex^2 โ^3 โค 1.
(a) x โค โ 2 or x โฅ 2 (b) โ 2 โค x โค 2 (c) x โค โ
3 or x โฅ
(d) โ
3 โค x โค
(e) x โค 2
9 (5 points). Find the solution set of the inequality log 2 (x + 1) < 2.
(a) x < 1 (b) x > โ 1 (c) x < 3 (d) โ 1 < x < 3 (e) โ 1 โค x < 3
10 (5 points). The complex number i^25 is equal to
(a) 5 i (b) 1 (c) i (d) โ 1 (e) โi
Part II: Partial Credit Problems
11 (10 points). Questions (a) through (d) refer to the graph of the function y = f (x):
x
y
1
1
y = f (x)
(a) Write the domain of f using the interval notation [a, b]:.
(b) Write the range of f using the interval notation [a, b]:.
(c) Find the average rate of change of f over its domain.
Solution.
(d) On which interval is f decreasing?
Answer.
12 (10 points). Let f (x) = x^2 + 3x and g(x) = x โ 2.
(a) Find f (โ2).
Solution.
(b) Find the difference quotient
f (x + h) โ f (x) h
. Simplify the answer.
Solution.
(c) Find (f โฆ g)(x). Simplify the answer.
Solution.
15 (14 points). Questions (a) through (d) refer to the function:
y = ln(x + 1) โ 1
(a) Graph the function y = ln(x + 1) โ 1.
x
y
1
1
(b) Write the domain and range of y = ln(x + 1) โ 1 using the interval notation [a, b].
Domain: Range:
(c) Find an equation of the vertical asymptote to the graph of y = ln(x + 1) โ 1.
Vertical Asymptote:
(d) Find the x- and y-intercepts of the graph of y = ln(x + 1) โ 1. Show all your work.
Solution.
x-Intercept: y-Intercept:
16 (9 points). Suppose that b is a positive constant greater than 1, and let A, B, and C be defined as follows: logb 2 = A logb 3 = B logb 5 = C
Use the properties of logarithms to evaluate each expression in terms of A, B, and/or C.
(a) logb 12
Solution.
(b) logb 0. 8
Solution.
(c) log 3 b 3
Solution.
17 (8 points). Solve the equation log 5 (x โ 1) + log 5 (x + 3) = 1 for x.
Solution.