Reference no: EM131665869
Assignment
Part 1
1. Solve the inequality x2 ≥ 7xand write the solution set in interval notation.
(no explanation required)
A. [7, ∞)
B. (-∞, 0] ∪ [7, ∞)
C. (-∞, 7] ∪ [0, ∞)
D. [0, 7]
2. Solve (x + 3)/(x^(2)- 7x + 6) ≤ 0 and write the solution set in interval notation.
(no explanation required)
A. (1, 6)
B. (-∞,-3]
C. (-∞,-3] ∪(1, 6)
D. [-3, 1) ∪ (6, ∞)
3. Forf(x) = x3 - 2x2 - 7, use the Intermediate Value Theorem to determine which interval must contain a zero of f.(no explanation required)
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
4. Translate this sentence about area into a mathematical equation.
The area A of a regular pentagon is directly proportional to the square of the length s of its sides.
5. Look at the graph of the quadratic function and complete the table.[No explanations required.] Graph Fill in the blanks Equation
Graph
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Fill in the blanks
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Equation
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![300_Graph.jpg](https://secure.expertsmind.com/CMSImages/300_Graph.jpg)
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State thevertex: ____________
State therange: _____________
State the interval on which the function is decreasing: _____
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The graph represents which of the following equations?
Choice:____
A. y = -x2+2x- 1
B. y = -2x2 - 4x + 1
C. y = 2x2+ 4x- 1
D. y = x2+2x- 1
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6. Each graph below represents a polynomial function. Complete the following table. (no explanation required)
Graph
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![922_Graph-A.jpg](https://secure.expertsmind.com/CMSImages/922_Graph-A.jpg) Graph A
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![768_Graph-B.jpg](https://secure.expertsmind.com/CMSImages/768_Graph-B.jpg) 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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7. LetP(x)=-x^3+4.5x^2-0.5x-6When factored,P(x)=-(x+1)(x-3/2)(x-4)
(a) State the domain.
(b) Which sketch illustrates the end behavior of the polynomial function?
![875_Polynomial-Function.jpg](https://secure.expertsmind.com/CMSImages/875_Polynomial-Function.jpg)
(c) State the y-intercept:
(d) State the real zeros:
(e) State which graph below is the graph of P(x).
![790_Graph-A-B-C-D.jpg](https://secure.expertsmind.com/CMSImages/790_Graph-A-B-C-D.jpg)
8. Let f(x) = (4x2 - 4) / (x2 - 9). (no explanations required)
(a) State the y-intercept.
(b) State the x-intercept(s).
(c) State the vertical asymptote(s).
(d) State the horizontal asymptote.
9. Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.
{(x + 1) / (x - 2)} - {6 / (x2 - 2x)} = 0
10. Which of the following functions is represented by the graph shown below? Explain your answer choice. Be sure to take the asymptotes into account in your explanation.
![1765_Graph1.jpg](https://secure.expertsmind.com/CMSImages/1765_Graph1.jpg)
A. f(x)= x^2/(x^2- 16)
B. f(x)= 3/(x^2- 16)
C. f(x)= (x )/(x^2- 4x)
D. f(x)= 3/(x^2+ 4x)
11. For z = 4 - 3i and w = 7 -i, find z/w. That is, determine (4 - 3i)/(7 - i) and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show work.
12. Consider the equation 5x2 + 20 = 16x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. Show work.
13. The cost, in dollars, for a company to produce x widgets is given by C(x) = 5250 + 7.00x for x≥ 0, and the price-demand function, in dollars per widget, is p(x) = 45- 0.02x for 0 ≤ x ≤ 2250.
In Quiz 2, problem #10, we saw that the profit function for this scenario is P(x) = - 0.02x2 + 38.00x - 5250.
(a) The profit function is a quadratic function and so its graph is a parabola.
Does the parabola open up or down? __________
(b) Find the vertex of the profit function P(x) using algebra. Show algebraic work.
(c) State the maximum profit and the number of widgets which yield that maximum profit:
The maximum profit is _______________ when ____________ widgets are produced and sold.
(d) Determine the price to charge per widget in order to maximize profit.
(e) Find and interpret the break-even points. Show algebraic work.
Part 2
Solve the following equation analytically:
1. 24x = 8
2. 3(x-1) = 27
3. 52x-1 = 125
4. 42x = 1/2
5. 8x = 1/128
6. 2(x^3-x) = 1
7. 37x = 814-2x
8. 9 · 37x = (1/9)2x
9. 32x = 5
10. 5-x = 2