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Sample Exam 1 |
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Find (p + q)(x) and the domain for p + q. Write the domain in interval or inequality form.
3. Let k(x) = -4(x - 10)1/2 + 3. The graph of k can be obtained by transformations of the graph of y = x1/2. These might include as a shift left or right, a shift up or down, a reflection in the x- or y-axis, stretching away from the x-axis or shrinking toward the x-axis by a certain factor. What are the transformations? 4. Solve the each of the following equations algebraically. Show all appropriate work. a. 2(x - 5)(2x + 3) + 2(x - 5)2= 0 b. 2x2/3 - 5x1/3 = 12 c. (y - 2)1/2 - (5y + 1)1/2 = -3 5. A farmer has 120 yards of fencing and wants to construct a rectangular pen, divided in two parts by an interior fence parallel to the shorter sides of the rectangle as shown in the figure. Your answer to this problem should include an identification of any variable used (e.g., x = length of dividing fence), an equation or equations and the algebra needed to answer the question. a. Write a function A(x) that gives the area of the outer rectangle (the total area of the pen) as a function of the length x of the interior fence. b. Suppose the farmer wants to enclose a total area of 450 square yards in the pen. What will the outer dimensions be? 6. The function h(t) = -16t2 + 144t + 576 gives the height (in feet) of a rock t seconds after it has been thrown upward. Draw the graph of h. Determine the maximum height of the rock and the time that it takes the rock to reach that maximum height. How do you know that there is a maximum height? Justify your answer. 7. Draw the graphs of the following functions. The x- and y-intercepts of each graph should be labeled with their values, any vertex should be labeled with its coordinates. Show each vertical or horizontal asymptotes with a dotted line and label it with its intercept value. a. y = | 3x - 9| b. y = x3 - 8
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