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Math 1113 Test III Study Guide: Functions, Logarithms, and Interest Rates - Prof. Allen G., Exams of Pre-Calculus

Gordon CollegePre-Calculus
Prof. Allen G. Fuller

This study guide provides solutions and explanations for various math problems in a university-level math 1113 course. Topics covered include finding vertical and horizontal asymptotes, identifying oblique asymptotes, graphing functions, solving equations, working with logarithms, and calculating compound interest.

Typology: Exams

Pre 2010

Uploaded on 08/04/2009

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STUDY GUIDE FOR TEST III
MATH 1113
1. Find the x-values where the following functions are discontinuous, identify
each as a vertical asymptote or missing point, find the horizontal asymptote
(if any). Find any oblique asymptote. Sketch a graph of the function. Plot
and label the x- and y-intercepts Use dashed lines to represent asymptotes.
(a) (b)
(c) (d)
(e)
Hint: The numerator factors. See Section R.5, Example 3, page 44.
(f)
2. Use translations (shifts) of and to graph the
following functions. State the domain and range. Identify any asymptotes.
(a) (b)
(c) (d)
(e) (f)
3. Solve the following equations.
(a) Solve without using your calculator.
(b) Solve without using your calculator.
(c) (d)
(e) (f)
(g) (h)
(i)
pf3
pf4
pf5

Partial preview of the text

Download Math 1113 Test III Study Guide: Functions, Logarithms, and Interest Rates - Prof. Allen G. and more Exams Pre-Calculus in PDF only on Docsity!

S TUDY G UIDE FOR T EST III

MATH 1113

  1. Find the x -values where the following functions are discontinuous, identify each as a vertical asymptote or missing point, find the horizontal asymptote (if any). Find any oblique asymptote. Sketch a graph of the function. Plot and label the x - and y -intercepts Use dashed lines to represent asymptotes.

(a) (b)

(c) (d)

(e)

Hint: The numerator factors. See Section R.5, Example 3, page 44.

(f)

  1. Use translations (shifts) of and to graph the

following functions. State the domain and range. Identify any asymptotes. (a) (b) (c) (d) (e) (f)

  1. Solve the following equations. (a) Solve without using your calculator.

(b) Solve without using your calculator.

(c) (d)

(e) (f)

(g) (h)

(i)

  1. Express the following as a single logarithm with a coefficient of 1. (a) (b)
  2. Rewrite each expression to have no logarithms except.

(a) (b)

(c)

  1. Rewrite each expression in terms of logarithms of x , y , and z.

(a) (b)

  1. Using algebra, find the domain of the following functions. Check your work on your graphing calculator.

(a) (b)

(c) (d)

  1. Antonia Lopez currently has $67,894 in a savings account that pays 5.22% annually interest compounded monthly. (a) If she neither deposits nor withdraws from the account, how much money will she have in seven years? (b) How much more would she have if the interest were compounded continuously?
  2. Kevin wishes to deposit $3,000 for a period of two years for a special purpose. After visiting several banks and investigating his options, he has selected three plans: A. 6.5% interest per year compounded daily B. 6.55% interest per year compounded monthly C. 6.6% interest per year compounded quarterly (a) Which plan will earn Kevin the most money? (b) How much will he lose if he chooses the worst plan?

Answers

1. ((a) v.a.: x = 1; x =! 1

h.a.: y = 0 x -int: none

y -int:! 1

(b) no points of discontinuity h.a.: y = 3 x -int and y -int: (0,0)

(c) v.a.: x = 1/2; x =! 1

h.a.: y = ½

x -int: !2, 3

y -int: 6

(d) v.a.: x = !2/3; x = 1

h.a.: y = 0 x -int and y -int: (0,0) (e) missing point: x = 3 x -int: none y -int: 9

(f) v.a.: x =! 2

o.a.: y = 2 x! 5

x -int: ,

y -int:! 4

  1. (a) D: all reals; R: ; h.a.: y = 1 (b) D: all reals; R: ; h.a.: y = 0 (c) D: all reals; R: ;

h.a.: y =! 2

(d) D: ; R: all reals; v.a.: x = 0 (e) D: ; R: all reals; v.a.: x = 2 (f) D: ; R: all reals;

v.a.: x =! 1

  1. (a) x = 3/

(b) x = !2/

(c)

(d)

(e)

(f) (g)

(h) x = 7 (i) x = 5/

  1. (a)

(b)

  1. (a)

(b) (c)

  1. (a) (b)
  2. (a) (b) (c) (d)
  3. (a) $97,763. (b) $77.
  4. (a) Plan C (b) $3.
  5. 6.8 years
  6. 33,715 bacteria
  7. 27,401 people
  8. approximately 192 mg
  1. 48.6 mg
  2. (a) u ( t ) = 34 + 41 e^ !0.056 t (b) 42°F (c) 54 minutes
    1. (a) u ( t ) = 14 + 57 e^ !0.609 t (b) 23°F (c) 3.7 minutes