Assignment
1. Solve using the Quadratic formula: x3 - 4x - 4 = 0.
A. 2
B. 2±2√2
C. 2±4√2
D. 4±2√2
2. Solve the equation: 9x4 - 10x2 + 1 = 0
A. 1/3, 1
B. ±1/3, ±1
C. 1/9, 1
D. ±1/3
3. Solve the rational equation: (3/2) - {1/(x-4)} = -2/(2x - 8).
A. x = 4
B. x = -4
C. x = 0
D. No solution
4. Solve the rational equation: {1/(x-2)} + {1 / (x -3) = 2 / (x - 2) (x - 3)
A. 2
B. 3
C. 4
D. 5
5. Solve the inequality. x2 - 6x ≤ 27
Write the solution using interval notation: 5.
A. (-3, 9)
B. (-∞, -3] ∪ [9, ∞)
C. [-3, 9]
D.[-9, 3]
6. Find the minimum or maximum value of f(x) = -x2 + 6x - 5, and give the coordinates of the vertex of the parabola.
A. Maximum = 3; vertex (3, 4)
B. Maximum = 4; vertex (4, 3)
C. Minimum = 4; vertex
D. None of the above
7. Find the Vertex and indicate the direction that the parabola opens: f(x) = x2 - 2x + 4
A. Vertex and Opens Up.
B. Vertex and Opens Up.
C. Vertex and Opens Down.
D. Vertex and Opens Down.
8. Simplify: i5
A. 1
B. -1
C. i
D. -i
9. Multiply: .
A.
B. 7
C.
D.
10. Express in the standard form a + bi: 5i / (1 + 2i)
A. (2/5) + (1/5)i
B. 2 + i
C. (1/5) - (2/5)i
D. 2 - i
11. Find the Vertical Asymptote: f(x) = (4 -x) / (2 + x)
A. x=2
B. x=-2
C. x=-4
D. x=4
12. Find the Horizontal Asymptote: f(x) = (4 -x) / (2 + x)
A. x=2
B. x=-2
C. x=-1
D. x=1
13. Let f (x) = -2x3+4x2-x+1. Use the Intermediate Value Theorem to determine which interval must contain a zero of f(x).
A. Between 0 and 1
B. Between 1 and 2
C. Between 2 and 3
D. Between 3 and 4
14. True or False: Let y=f(x) be a polynomial function. The x-intercepts of the function f(x) are the roots of the equation f(x) = 0.
15. True or False. Let y=f(x) be a polynomial function of degree 3.
The function y=f(x) must have at least one real root.
16. True or False. It is possible for a quadratic equation with real coefficients to have one real and one complex root.
17. Consider the graph of the polynomial y=p(x). Answer the following questions. (No explanation needed)
![1001_Graph.jpg](https://secure.tutorsglobe.com/CMSImages/1001_Graph.jpg)
(a) Is the degree of p(x) even or odd?
(b) Is the leading coefficient positive or negative?
(c) How many real number zeros are there?
18. Let f(x) = (2x2 - 2) / (x2 - 4) (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.
(e) Draw the graph. Show the asymptotes.
19. Translate this sentence about area into a mathematical equation.
The area A of a regular hexagon is directly proportional to the square of the length s of its side.
20. Find all solutions, real and complex, of the equation x2-4x+5=0.
Simplify as much as possible and clearly show all the steps.