Directions: Read each problem carefully. The point value for each section is marked. Multiple-Choice: Read each problem carefully and write the letter of the best choice in the blank
provided. Each problem is worth 1 point. _____1.Determine whether or not the function is one-to-one: a Yes b No c. not enough information _____2.Determine whether or not the function a Yes b No f ( x ) 2e x 4 is one-to-one: c. not enough information _____3.Determine whether or not the functions f(x) and g(x) are inverses of each other. f = {(-2, -4), (1, 4), (4, -2), (8, 11)}
g = {(-4, -2), (4, 1),(-2, 4), (11, 8)} a Yes b No c. not enough information _____4.Determine whether or not the matrices A and B are inverses of each other. 5 3 A 3 2 a Yes b No and 2 3
A 3 5 c. not enough information _____5. Determine the value of a 2.5850 log 2 6 : b. 5.2700 c. -2.5850 d. 0.3869 e. None of these Short Answer: Read each problem carefully and write your answer in the space provided. Show your
relevant work and circle your final answer to receive full credit. Each part is worth 2 points unless
marked otherwise. 6. Find the inverse functions if they exist, if they don’t exist explain why: a. F = { (2, 5), (3, 4), (4, 1), (0, -1), (1, 6) } b. f ( x) 5x
x 2 7.
For each function, give the domain, range, intercepts, equation of asymptote, and find the
inverse.
(6 points each) a. f ( x) log( x 1) The domain is ________________ The range is_____________________ The x-intercept is _____________ The asymptote is ________________ The y-intercept is _____________ The inverse is ___________________ b. f ( x) 3 x 2 The domain is ________________ The range is_____________________ 8. The x-intercept is _____________ The asymptote is ________________ The y-intercept is _____________ The inverse is ___________________ Simplify the expressions as much as possible: a. = 6 ln ( e ) b. 8 log 2 x = c. = 1 log b b2 d. 10 2 log x = e. e ln x x ln e 9.
Suppose the following augmented matrices were produced by applying the Gauss-Jordan
method to a system of equations. Derive or explain in detail what you can about the solutions of the
systems. a. 1 0
0 0 0 1 b. 0 | 5
0 | 3
0 | 4 1 0 1 | 4
0 1 2 | 3 0 0 0 | 0 Workout: Read the following problems carefully. Show your relevant work and circle your answers to
receive full credit. Each problem is worth 2 points unless marked otherwise. 10. Solve the exponential equations: a. 1
4 x 1 16 b. 2 e 3 x 1 7 19 11. a. Solve the logarithmic equations: log 5 ( x 4) 2 0 b. 2 ln 2 x 2 ln ( 2 x ) 1 0 12. Recall, the formula for an account paying interest compounded continuously is A Pe
How long will it take to double your money if such an account pays 6.5% ? rt . 13.
Solve the system of equations. Make sure that you show the appropriate supporting work and
state what your final solution is to receive full credit. a. 3 x y 23
3 y 8 14 b. 6 y 4 x 1
6 x 9 y 2 14. Find a pair of matrices which may be multiplied, and circle below that arrangement. Then
carry out the multiplication in the space below: a 1
1 1
3 1
2 0 2 , D 1 b
A 2 a 3 1 , B 2 0 , C 3 a
1
1 2 4 3 2 2 4 AB AC AD BA CA DA BC BD CB DB CD DC 15.
Solve the system of equations using a matrix equation and your calculator. Write down the
augmented matrix or matrix equation and then final solution from calculator. x1 x2 x3 x4 x5 3 2 x1 x2 x3 x4 x5 2 x1 x1 2 x2 x2 x4
x4 2 x5 x5 11 3 2 x1 x3 3 x3 x3 x5 5 x2 2 x4

 

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