Assignment
1. Solve {(x + 3) (2 - x)} / (x - 1)2 > 0 and write interval notation for the solution set.
Show careful algebraic work/explanation.
2. For f(x) = x3 - 4x - 8, use the Intermediate Value Theorem to determine which interval must contain a zero of f(x). (no explanation required) 5. ______
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
3. Look at the graph of the quadratic function and state the intercept(s), vertex, and range, and indicate which of equations A, B, C, or D, represents the graph. [No explanations required.]
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Graph
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Fill in the blanks
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Equation
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State the y-intercept(s): ___________
State thevertex:
___________
State therange:
_________
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The graph represents which of the following equations?
Choice: __
A. y = x2 - 6x + 1
B. y = -x2 - 6x + 1
C. y = x2+6x+1
D. y = -x2+6x + 1
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4. Each graph below represents a polynomial function. Complete the following table.
(no explanation required)
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Graph
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Graph A
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Graph B
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Is the degree of the polynomial odd or even?(choose one)
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Is the leading coefficient of the polynomial positive or negative? (choose one)
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How many real number zeros are there?
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5. (No explanations required)
Let P(x) = x3 - (21/4)x + (5/2) When factored, P(x) = {x + (5/2)} {x - (1/2)} (x - 2)
(a) State the domain.
(b) Which sketch illustrates the end behavior of the polynomial function?
(c) State the y-intercept:
(d) State the x-intercepts:
(e) State which graph below is the graph of P(x).__________________
6. Let f(x) = (3x2 - 3x) / (x2 + x - 12) (no explanation required)
(a) State the domain.
(b) State the y-intercept.
(c) State the x-intercept(s).
(d) State the vertical asymptote(s).
(e) State the horizontal asymptote.
7. Solve the equation. Show work in solving
{1 / (5x + 20)} - {1 / (x2 - 16)} = {3 / (x - 4)}
8. For z = 5 + 2i and w = 8 - 3i, find z/w. Simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show work.
9. Find the solutions of the equation 4x2 - 8x + 7 = 0. Show algebraic work.
10. The marketing department has found that, when the new model calculators are sold at a price of p dollars per unit, the revenue R (in dollars) as a function of the price is:
R(p) = -150p2 + 21,000p
(a) The revenue function is a quadratic function and so its graph is a parabola.
Does the parabola open up or down? _________
(b) What unit price should be established in order to maximize revenue?
(c) If this price is charged, what is the maximum revenue?