(10 pts) Let f (x) = 2x2 – x – 9 and g(x) = 4x + 1 (a) Find the composite function and simplify the results. Show work. (b) Find . Show work.
2. (5 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.
3. (5 pts) Solve £ 0 and write the solution set in interval notation. 2. ______
(no explanation required)
C.(–¥, –3] È (1, 6)
D.[–3, 1) È (6, ¥)
4. (10 pts) Look at the graph of the quadratic function and complete the table. [No explanations required.]
Fill in the blanks
State the vertex:
State the range:
State the interval on which the function is decreasing:
The graph represents which of the following equations?
A. y = –x2 + 2x – 1
B. y = –2x2 – 4x + 1
C. y = 2x2 + 4x – 1
D. y = x2 + 2x – 1
5. (10 pts) Let . (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.
6. (15 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.
7. (10 pts) 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.
8. (10 pts) For z = 4 - 3i and w = 7 - i, find z/w. That is, determine and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers. Show work.
9. (10 pts) 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.
10. (15 pts) The cost, in dollars, for a company to produce x widgets is given by C(x) = 5250 + 7.00x for x ³ 0, and the price-demand function, in dollars per widget, is p(x) = 45 - 0.02x for 0 £x £ 2250.
The profit function for this scenario is
P(x) = - 0.02x2 + 38.00x - 5250. AND C(300)
(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.