MHF Test 1 Wednesday September 24, 2008

1.Given a function defined by f(x) = x4 - 6x2 - 2.

a. (KU 2) Determine the average rate of change of f between x = 1 and x = 2.

b. (KU 4)Determine the instantaneous rate of change of f at x = 1 by successive approximations. Demonstrate your understanding of this process in the table provided. (Your calculator may be used to assist with values to be written in the table.) Be sure to include headings for your columns. Explain.

c. (KU 3) Demonstrate graphically the process you used in part “b” to determine the instantaneous rate of change of f at x = 1 given the graph of f(x) = x4 - 6x2 - 2. Explain.

2.(KU 4) a. Determine an algebraic representation of the following piecewise function.

b. Is this a function which is continuous? If not, explain where there are discontinuities within the given domain, .

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3.(A 3) The graphs of f and g are shown below. Sketch the graph of f + g on the same axes.

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4. Given g(x) =

(KU 3) Determine the equation for the inverse function.

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5.(A 3) Sketch a graph, of a function, with the following characteristics: symmetric with respect to the y-axis; vertical asymptote at x = -1; horizontal asymptote at y = 1; and decreasing on the interval x > 3.

6.(App 3) Draw a distance versus time graph that corresponds to the walk described below. Adam starts 8 m away from the motion sensor and walks in a straight line toward the sensor at a constant rate of 0.5 m/s for 3 s. He immediately begins walking away from the sensor at a constant rate of 0.25 m/s for 4 s. He stops for 1s and then walks toward the sensor at a constant rate of 0.5 m/s for 2 s.

7.(App 5) The sales of a new children’s book at a local book store are shown in the table below. The time represents the number of weeks after the book first went on sale.

Week / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9
Books Sold / 3 / 10 / 15 / 18 / 19 / 18 / 15 / 10 / 3

a. Create a model for this data (using the TI-83).

b. Use an algebraic strategy to determine an expression for the slopes of the secants which occur when calculating the instantaneous rate of change in the number of books sold at 7 weeks.

c. Determine the instantaneous rate of change in the number of books sold at 7 weeks.

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8.(App 2) Determine a function whose domain is {x R}which is both even and odd. Justify your answer.