1. (4 pts) Solve the inequality x2 2x and write the solution set in interval notation.
(no explanation required) 1. ______
A. (–, 0] [2, )
B. [0, 2]
C. (–, 2]
D. (–, 2] [0, )
2. (4 pts) Solve 0 and write the solution set in interval notation. 2. ______
(no explanation required)
A. (2, 5)
B. (–, –1]
C. (–, –1] (2, 5)
D. [–1, 2) (5, )
3. (4 pts) For f (x) = x3 – 3x2 – 8, use the Intermediate Value Theorem to determine which interval must contain a zero of f. (no explanation required) 3. _______
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
4. (4 pts) Translate this sentence about stopping distance into a mathematical equation.
With the application of a car’s brakes, the stopping distance d of the car is directly proportional to the square of the speed s.
5. (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 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 – 2
B. y = –x2 + 2x – 2
C. y = 2x2 – 3x – 2
D. y = –2x2 + x – 2
6. (6 pts) Each graph below represents a polynomial function. Complete the following table.
(no explanation required)
|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?|
7. (12 pts) Let
(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)
(a) State the y-intercept.
(b) State the x-intercept(s).
(c) State the vertical asymptote(s).
(d) State the horizontal asymptote.
9. (8 pts) Solve the equation. Check all proposed solutions. Show work in solving and in checking, and state your final conclusion.
10. (8 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.
11. (8 pts) For z = 8 i and w = 1 2i, 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.
12. (8 pts) Consider the equation 5x2 + 5 = 8x. Find the complex solutions (real and non-real) of the equation, and simplify as much as possible. Show work.
13. (18 pts)
The cost, in dollars, for a company to produce x widgets is given by C(x) = 3600 + 5x for
x 0, and the price-demand function, in dollars per widget, is p(x) = 45 0.04x for 0 x 1125.
In Quiz 2, problem #10, we saw that the profit function for this scenario is
P(x) = 0.04x2 + 40x 3600.
(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.
14. Interpret your results in part (a), in the context of the application involving fish.
The cost C in dollars to remove p% of the invasive species of Ippizuti fish from Sasquatch Pond is given by
(a) Find and interpret C(25) and C(95).
(b) What does the vertical asymptote at x = 100 mean within the context of the problem?
(c) What percentage of the Ippizuti fish can you remove for ✩40000?