Download Math 140, Exam V: Rational Functions, Logarithms, and Interest Rates - Prof. Louis Kolitsc and more Exams Mathematics in PDF only on Docsity!
Math 140, Exam V, Version A Name _________________________
There are 7 problems on this exam. Carefully read and follow all directions. In order to receive credit show all necessary work. No credit will be given for an answer I cannot find or cannot read.
- Match the following rational functions with their descriptions given below. Each question has one correct answer. However, the functions may be used more than once. (2 points each)
A(x) =
2 2
x x x
) (^) B(x) =^2 2
x x x
C(x) =
3 2 2
x x x
D(x) =
3 2 2
x x x
E(x) = 22 6 5 6
x x x
F(x) =
2 2
x x
(a) Has the line y = 2 as an asymptote
(b) Has (โ3, 0) as an x-intercept
(c) Has the x-axis as an asymptote
(d) Has the line x = 2 as an asymptote
(e) Rises on the left and falls on the right
(f) Passes through the origin
(g) Has domain ( โโ, โ )
(h) Has no x-intercept
(i) Touches but does not cross the x-axis at the point (2, 0)
(j) Has y-intercept (0, 1)
(k) Has no vertical asymptote
- Let f(x) = โlog 4 (x + 16). Determine each of the following. If the function does not have a particular feature, write NONE. (3 points each)
(a) Domain of f
(b) Range of f
(c) x-intercept(s) on graph of f
(d) y-intercept on graph of f
(e) horizontal asymptote on graph of f
(f) vertical asymptote(s) on graph of f
(g) Is the function f increasing or decreasing?
(h) Describe using shifts and/or reflections how the graph of y = f(x) is related to the graph of y = log 4 (x).
- $2000 is invested in an account earning 6% annual interest compounded continuously. Determine the following.
(a) What will be the value of the account after 3 years? (5 points)
(b) How long will it take the account to reach a value of $3500? Round your answer to two decimal places. (5 points)
- $500 is invested in an account earning 3% annual interest compounded monthly. Determine the following.
(a) What will be the value of the account after 3 years? (5 points)
BONUS (b) How long will it take the account to reach a value of $1500? Round your answer to two decimal places. (5 points)
- Let r(x) = log 3 (x + 4) โ log 3 (x โ 2) โ 2.
(a) Determine the domain of r(x). (3 points)
(b) Where is the x-intercept on the graph of y = r(x) located? (3 points)
- Let h(x) = log 3 (x + 27) โ 2 log 3 (x + 9) โ 3log 3 (x + 1)
(a) Determine the domain of h(x). (3 points)
(b) Use the properties of logarithms to express h(x) as a single logarithm. (3 points)
(c) Where is the y-intercept on the graph of y = h(x) located? (3 points)
