I have 10 algebra problems that I need done with one bonus problem which is option. Nedd to have done by 12/2/12
MATH 107
• Show work/explanation where indicated. 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 also acceptable. In your document, be sure to include your name and the assertion of independence of work.
1. Solve and write interval notation for the solution set. Then graph the solution set Show your work. (14 pts)
a)
. |3x + 4| < 13
b)
.
2. For each polynomial function find the following:
i) Find the rational zeros and then the other zeros. (4 pts)
ii) Factor f(x) into linear factors (4 pts)
a)
b)
3. Find the zeros of the polynomial function and state the multiplicity of each. Show your work. (8 pts)
a)
4. Determine whether the statement is true or false. Show your work. (8 pts)
a) If , then the graph of the polynomial function crosses the x-axis at (True or False
b) ) If , then the graph of the polynomial function is tangent the x-axis at (4True or False
(Hint: A curve tangent point is a point within the curve)
5. Using the leading-term test, match each of the following functions with one of the graphs A-D and fill out the table provided. (Hint: Using the leading-term test find whether at the leading term, n is even or odd and is positive or negative. Keep the following key graphs in mind
Key graphs: ) (16 pts)
Functions:
a)
b) )
c)
d)
Graphs:
Graph A:
y
Graph B:
y
Graph C:
y
Graph D:
y
Function
Leading Term
Degree of Leading Term
Sign of Leading Coefficient
Graph
(Choose A,B, C or D)
b)
c)
You can use the additional space below for your work on Q5.
6. Equation, graph, domain, x and y intercept information of two functions are given below. Find whether the following statements regarding the functions are true or false. Show your work. (14 pts)
a)
y
· The graph given belongs to function f(x): True or False.
· The function f(x) has two vertical asymptotes which are defined by x = -4 and x = 3: True or False
· The x intercept of the given function f(x) is at (-4, 0): True or False
(Hint: f(x)=0 solve for x)
· The y intercept of the given function f(x) is at (0,): True or False (Hint: f(x)=? for x=0)
· The domain of the given function f(x) is (-∞,) U (-1,3) U (3, ∞): True or False
b)
y
· The graph given belongs to function g(x): True or False
· The function g(x) has only one vertical asymptote defined by x= -6: True or False
· The x intercept of the given function g(x) is none: True or False
(Hint: g(x)=0 solve for x for real numbers)
· The y intercept of the given function f(x) is at (0,): True or False (Hint: g(x)=? for x=0)
· The domain of the given function g(x) is (-∞,) U (-1, ∞): True or False
7. Solve the following polynomial inequality. Show your work. (8 pts)
a)
8. The graph of function f is which one of the following. Show your work. (6 pts)
9. The graph of function f is which one of the following. Show your work.(6 pts)
10. The equations of functions are given below. State whether each statement is true or false. Show your work. (12 pts)
a)
The graph belongs to function f(x): True or False
b)
The graph belongs to function g(x): True or False
c)
The graph belongs to function h(x): True or False
Bonus Question: The graph of the system defined by the two inequalities given below is which one of the following? (6 pts )
Inequalities:
