Pre-Calculus homework

MATH 115 QUIZ 2 November, 2019 Instructor: I. Izmirli

NAME: _______________________________

I have completed this assignment myself, working independently and not consulting anyone except the instructor.

INSTRUCTIONS

· The quiz is worth 100 points. There are 10 problems.

· Each problem is worth 10 points

· This quiz is open book and open notes . This means that you may refer to your textbook, notes, and online classroom materials, but you must work independently and may not consult anyone (and confirm this with your submission). You may take as much time as you wish, provided you turn in your quiz no later than this Sunday.

· Show work/explanation. Answers without any work may earn little, if any, credit. You may type or write your work in your copy of the quiz, or if you prefer, create a document containing your work. Scanned work is acceptable also. In your document, be sure to include your name and the assertion of independence of work.

· General quiz tips and instructions for submitting work are posted in the Quizzes module.

· If you have any questions, please contact me by e-mail.

1. Which of the following equations does the graph represent?

A. B. C. D.

C

The answer is C, because points that are plotted from the equation is (0,6) and (1,6.9)

2. Consider the points (– 2, 1) and (4, -3).

(a) Find the slope-intercept equation of the line passing through the two given points. Show work.

(b) Graph the line you found in (a).

3. Find the equation of the line that passes through the point (1, 1) and is perpendicular to the line you obtained in problem 2

4. The amount of gas g in gallons in a car's gas tank t days after a fill-up is modeled by g(t) = –0.5t2 – 1.5t + 20 for 0 ≤ t ≤ 4.

Find and interpret the average rate of change of g over the interval [0, 4].

5. Look at the graph of the quadratic function and complete the table.

Graph	Fill in the blanks	Equation
	(a) State the vertex: ____________ (b) State the range: _____________ (c) State the interval on which the function is increasing: _____________	(d) The graph represents which of the following equations? Choice:____ A. y = –x2 + 4x – 3 B. y = –2x2 – x + 3 C. y = x2 – 2x – 3 D. y = x2 + 2x – 3

6. Look at the graph of the polynomial function and complete the table.

Graph

Fill in the blanks

(a) State the y-intercept: ________________ (b) State the real-number zeros: ___________________ (c) Is the degree of the polynomial odd or even? (choose one) (d) Is the leading coefficient of the polynomial positive or negative? (choose one) (e) The graph represents which of the following polynomials, shown in factored form? Choice:____ A. f (x) = – 0.2(x + 3)(x + 1)(x – 2)(x –5) B. f (x) = 0.2(x + 3)(x + 1)(x – 2)(x –5) C. f (x) = – 0.2(x –3)(x – 1)(x + 2)(x + 5) D. f (x) = 0.03(x – 6)(x –3)(x – 1)(x + 2)(x + 5)

7. Solve the inequality x2 ≥ 3x and write the solution set in interval notation.

A. (–∞, 3]

B. (–∞, 0] ∪ [3, ∞)

C. (–∞, 3] ∪ [0, ∞)

D. [0, 3]

8. For f (x) = x3 – x2 – 2, use the Intermediate Value Theorem to determine which interval must contain a zero of f.

A. Between 0 and 1

B. Between 1 and 2

C. Between 2 and 3

D. Between 3 and 4

9. For z = 4 + 3i and w = 5 - 2i, find zw. That is, determine (4 + 3i) (5 - 2i) and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers.

10. For z = 8 + 3i and w = 7 + 2i, find . That is, determine (8 + 3i) / (7 + 2i) and simplify as much as possible, writing the result in the form a + bi, where a and b are real numbers.