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1. Let
 g(x) = 2- x3 + 4x and h(x) = 7x2
1. Find (g o h)(x) (don't forget to simplify).
2. Find the inverse of g. Label your answer clearly either as "the inverse of g" or with "g-1(x) = ... .

1. Find the domain of the function k defined by k (t) = (5 - t)1/2 + ln (t + 3) + 3t-2
2. The graph of a function h is created by shifting the graph of y = 2x to the right 5 units, then reflecting it in the x-axis, 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.

2. 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.
1. x + 2y2 = 0
2. 9x2 + y2 = 36

3. Solve each of the following equations for x (exact values):
1. 3 log5 (4x - 1) = 1/2
2. 105 (85x+3) = 315

1. Write as a single logarithm and simplify: 4 ln (s + 2) - 3 ln (s2 - 4) + ln (s + 1)
2. Show the tail behavior and behavior at x = 2 for each of the following polynomials:
1. f is a fifth-degree polynomial with five different x-intercepts including
x = 2 and f(x) < 0 for x > 2
2. g is an eighth-degree polynomial with x-intercept 2 and g(x) > 0 for x > 1

4. For each of the following the answers must be exact.
1. Write without logarithms and negative exponents: log4 (cube-root of 16) + e-3 ln x
2. 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 x2 (x + 1)1/2(x2 + 2x + 1)1/2

5. Let
 g(x) = (x - 3)2(x + 4)(12 - 3x)
.
1. Find (i) the x- and y-intercepts 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.
2. Use a table of signs to solve the inequality
 (x - 3)2(x + 4)(12 - 3x) > 0
.

6. 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 = 3p4 4p3 11p6 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

1. Convert the angle 780o to radians.