


If your browser is not reading the directions for the Symbol font, you will see the letter "p" instead of the Greek letter pi.
 Let
g(x) =  2 x 3 + 4x  and  h(x) =  7 x^{2} 
 Find (g o h)(x) (don't forget to simplify).
 Find the inverse of g. Label your answer clearly either as "the inverse of g" or with "g^{1}(x) = ... .

 Find the domain of the function k defined by k (t) = (5  t)^{1/2} + ln (t + 3) + 3t^{2}
 The graph of a function h is created by shifting the graph of y = 2^{x} to the right 5 units, then reflecting it in the xaxis, and then shifting it up 10 units. Draw the graph of h and find h(x). Show and label with its intercept or equation any asymptote.
 Draw and name the graph of each of the following equations. On your graph label with their coordinates all vertices and intercepts. Label any asymptote with its equation. Indicate clearly the scale on all axes.
 x + 2y^{2} = 0
 9x^{2} + y^{2} = 36
 Solve each of the following equations for x (exact values):
 3 log_{5} (4x  1) = 1/2
 105 (8^{5x+3}) = 315

 Write as a single logarithm and simplify: 4 ln (s + 2)  3 ln (s^{2}  4) + ln (s + 1)
 Show the tail behavior and behavior at x = 2 for each of the following polynomials:
 f is a fifthdegree polynomial with five different xintercepts including
x = 2 and f(x) < 0 for x > 2
 g is an eighthdegree polynomial with xintercept 2 and g(x) > 0 for x > 1
 For each of the following the answers must be exact.
 Write without logarithms and negative exponents: log_{4} (cuberoot of 16) + e^{3 ln x}
 Use the properties of logarithms to simplify the following expression so that the result does not contain logarithms of products, quotients or powers. Assume x > 0.
ln  x^{2} (x + 1)^{1/2} (x^{2} + 2x + 1)^{1/2} 
 Let
g(x) =  (x  3)^{2} (x + 4)(12  3x)  .
 Find (i) the x and yintercepts and (ii) the vertical and horizontal asymptotes for the graph of g. Label your answers clearly. If the graph of g does not have one of the intercepts or asymptotes write NONE for that item.
 Use a table of signs to solve the inequality
(x  3)^{2} (x + 4)(12  3x)  > 0  .
 Fill in each of the empty cells (those with no x's) in the following table. If a value does not exist write DNE in the cell. Notice that in the last column cos t = 5/7 with  p/2 < t < 0.
>
t =  3p 4  4p 3  11p 6  angle with  p/2 < t < 0 
sin t  xxxxx  xxxxx  ______  _____ 
cos t  ______  ______  ______  5/7 
tan t  xxxxx  ______  ______  _____ 
sec t  xxxxx  xxxxx  xxxxx  _____ 
csc t  _____  xxxxx  xxxxx  xxxxx 

Convert the angle 780^{o} to radians.
 In what quadrant does the terminal side of an angle of 5 radians lie? Justify your answer.
 Let sin u = 2/5 and p/2 < x < p. Find each of the following (exact values).
 cos (u + 7p/6)
 sin (u  2p/3)

 Show that the expression
(sin t  cos t)(sin t + cos t) 2 sin t cos t 
can be simplified to a multiple of cot 2t.
 Find all solutions for x (exact values in radians): 2 cos 3x sin x + 3^{1/2} cos 3x = 0
 Joel wants to determine the height of a hot air balloon that is sitting on the ground. Using a surveyor's transit that is 5 feet above the ground he stands at a point A and measures the angle of elevation of the top of the balloon as 16.3°. He then walks 30 feet straight toward the balloon to a point B and again using the transit measures the angle of elevation of the top of the balloon as 18.5°. Draw a picture illustrating this situation, marking clearly all known angles and distances and any variable(s) used in solving the problem. State clearly any equation(s) used (there must be at least one). Then find the height of the balloon (to the nearest foot). Give a complete answer (The height of the balloon is ...).
