- (4 pts) Solve the inequality x2 ³3xand write the solution set in interval notation.Show work.
- (4 pts) Solve £ 0 and write the solution set in interval notation.Show work.
- (4 pts)Forf (x) = x3 + 3x2 – 6, use the Intermediate Value Theorem to determine which interval must contain a zero of f. Show work.
- Between 0 and 1
- Between 1 and 2
- Between 2 and 3
- Between 3 and 4
- (4 pts)Translate this sentence about volume into a mathematical equation.
The volume Vof wood is directly proportional to the height h and the square of the girth g.
- (8 pts)Look at the graph of the quadratic function and complete the table.No explanations required.
|Graph||Fill in the blanks||Equation|
State the interval on which the function is decreasing:
The graph represents which of the following equations?
A. y = –x2 + 2x+ 6
B. y = –2x2 – 4x+ 6
C. y = 2x2 + 4x – 6
D. y = x2– 2x – 6
- (6 pts)Each graph below represents a polynomial function. Complete the following table.
No explanations required.
|Graph A||Graph B|
|Is the degree of the polynomial odd or even? (choose one)|
|Is the leading coefficient of the polynomial positive or negative? (choose one)|
|How many real number zeros are there?|
- (12 pts) Let When factored, .
(a) State the domain.
(b) Which sketch illustrates the end behavior of the polynomial function?
(c) State the y-intercept:
(d) State the real zeros:
(e) State which graph below is the graph of P(x).
GRAPH A (below) GRAPH B (below)
GRAPH C (below) GRAPH D (below)
- (8 pts)Let .
(a) State the y-intercept.
(b) State the x-intercept(s).
(c) State the vertical asymptote(s).
(d) State the horizontal asymptote.
- (8 pts)Solve the equation.Check all proposed solutions.Show work in solving and in checking, and state your final conclusion.
- (8 pts) Which of the following functions is represented by the graph shown below? Explain your answer choice (provide some work or state a theorem used to draw your conclusion). Be sure to take the asymptotes into account in your explanation.
- (8 pts)Forz = 2-5i and w = 1-6i, find z/w. That is, determine and simplify as much as possible, writing the result in the form a + bi, where a andb are real numbers. Show work.
- (8 pts)Consider the equation 25x2 + 1 = 6x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible.Show work.
- (18 pts)
The cost, in dollars, for a company to produce x widgets is given by C(x) = 6x+ 3600 for
x³ 0, and the price-demand function, in dollars per widget, is p(x) = 50- 0.02x for 0 £x£ 2500.
In Quiz 2, problem #10, we saw that the profit function for this scenario is:
P(x) = – 0.02x2 + 44x -3600
(a) The profit function is a quadratic function and so its graph is a parabola.
Does the parabola open up or down (explain why)? __________
(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. Round answer to nearest whole number.Show work.
- (6 pts) The faucet in Nancy’s house can fill the sink in 6 minutes, while the drain can empty the same sink in 9 minutes. If her son, Tommy, turns the faucet on and leaves the drain open, how much time does Nancy have to discover the open faucet before the sink is filled and starts to overflow? In other words, how long will it take to fill the sink (in which case, Nancy will have a mess on her hands)?
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