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MATH Questions Show work/explanation where indicated 1. (4 pts) Solve the inequality x2 9x and write the solution set in interval notation.
(no explanation required) A.
B.
C.
D. 2. (4 pts) Solve 1. ______ [0, 9]
[9, )
(–, 9] [0, )
(–, 0] [9, )
x+ 6
x −6 x +8 2 0 and write the solution set in interval notation. 2. ______ (no explanation required) A.
B.
C.
D. [–6, 2) (4, )
(–, –6] (2, 4)
[–6, )
(2, 4) 3. (4 pts) For f (x) = x4 – 4x2 – 9, 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.
The area A of a regular hexagon is directly proportional to the square of the length s of its sides. 5. (8 pts) Look at the graph of the quadratic function and complete the table.
Fill in the blanks Graph State the vertex:
____________
State the range:
_____________
State the interval on
which the function
is decreasing:
_____________ [No explanations required.]
Equation The graph represents
which of the following
equations? Choice:____
A. y = –x2 + 2x – 1
B. y = 2x2 + 4x – 1 C. y = x2 + 2x – 1 D. y = –2x2 – 4x + 1 6. (6 pts) Each graph below represents a polynomial function. Complete the following table.
(no explanation required) Graph Graph A 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? Graph B P ( x )=−0.50 x 3 +1.75 x 2 +1.75 x−3 Let 7. (12 pts) When factored, ( 32 ) ( x−1) ( x−4 ) P ( x )=−0.5 x+ (a) State the domain.
(b) Which sketch illustrates the end behavior of the polynomial function? A. B.
vvvv C.
vvvv D.
vvvv vvvv (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) Answer: ________ 8. (8 pts) Let 2 f ( x) . (no explanations required) 4x 4
x 2 49 (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. x 3
40 2
0
x 8 x 8x 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. 10. _____
2 A. f ( x )= x −4
x −2 x−3 B. f ( x )= x −4
2
x +2 x−3 f ( x )= x
x −2 x−3 f ( x )= x
x +2 x−3 2 2 C. D. 2 2 11. (8 pts) For z = 9 + 2i and w = 3 5i, find z/w. That is, determine 9+2 i
3−5 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. (8 pts) Consider the equation 13x2 + 2 = 10x. Find the complex solutions (real and nonreal) 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) = 4200 + 5x for
x 0, and the price-demand function, in dollars per widget, is p(x) = 32 0.03x for 0 x 1066.
In Quiz 2, problem #10, we saw that the profit function for this scenario is
P(x) = 0.03x2 + 27x 4200.
(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.

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