- (4 pts) Solve the inequality x2 £ 2x and write the solution set in interval notation.
(no explanation required) 1. ______
- (–¥, 0] È [2, ¥)
- [0, 2]
- (–¥, 2]
- (–¥, 2] È [0, ¥)
- (4 pts) Solve £ 0 and write the solution set in interval notation. 2. ______
(no explanation required)
- (2, 5)
- (–¥, –1]
- (–¥, –1] È (2, 5)
- [–1, 2) È (5, ¥)
- (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. _______
- Between 0 and 1
- Between 1 and 2
- Between 2 and 3
- Between 3 and 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.
- (8 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 – 2
B. y = –x2 + 2x – 2
C. y = 2x2 – 3x – 2
D. y = –2x2 + x – 2
- (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?
- (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)
- (8 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.
- (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. Be sure to take the asymptotes into account in your explanation.
- (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.
- (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.
- (18 pts)
The cost, in dollars, for a company to produce x widgets is given by C(x) = 3600 + 5x for
x ³ 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.
- 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?