Algebra Answers

1: Which of the following expressions is this one equivalent to?

4x^3 + 2x^2 + x + 3
-------------------------
x + 2

A: 4x^3 – 6x + 13 + 23/x + 2

B: 4x^2 – 6x + 13 – 23/x + 2

C: 4x – 6 + 13/x + 2

D: 4x^2 + 13 – 2/x + 2

2: Which of the following expressions is this one equivalent to?
(x^4 -2x^3 + x – 2) divided by (x^3 + 1)

A: x^2 – x + 1

B: x^2 + 1

C: x^2 + 3x + 2

D: x – 2

3: What is the remainder when x^2 + 3 is divided by x -1 ?
Answer ______

4: Evaluate f(1) using substitution: f(x) = 2x^3 – 3x^2 – 18x + 8
Answer: ______

1: The graph of y = 3x^2 -4x + 2 opens downward.
A: True
B: False

2: The graph of y = 2x^2 -4x – 2 has a y-intercept of (0,2)
A: True
B: False

3: What is the axis of symmetry for the graph of y = 2x^2 – 8x + 2?

x = _______ __________



4: What is the vertex for the graph of y – 4 = -(x + 1)^2 ?

A: (4,-1)
B: (1,-4)
C: (-1,4)
D: (-4,1)

5: What are the x-intercepts for the graph of y=3(x-1)(x+6)

A: (-1,0) and (6,0)
B: (1,0) and (-6, 0)
C: (0, -1) and (0,6)
D: (0,1) and (0,-6)

9: What is the vertex of the graph of this function?
Y = -(x+2)(x+4)

A: (-2,-4)
B: (3,-35)
C: (-3,1)
D: (-3,-1)

10: The point (-1,0) lies on the graph of the function y = 2x^2 -8x + 6
A: True
B: False

5: Which of the following represents this function written in standard form. There can be multiple right answers. Check all that apply.
Y= 2(x+1)(x-6)

Y=2x^2 - 10x - 12

Y= 2x^2 - 10x +6

Y= 2x^2 -5x -12

Y=2x^2 -14x +12
---------------------------------------...
6: Which of the following represents this function written in intercept form? There can be multiple right answers. Check all that apply.
Y = - x^2 – x + 6

y = -(x – 2)(x + 3)

y = -(x + 2)(x – 6)

y = -(x + 2)(x + 6)

y = (-x + 3)(x – 4)

7: What are the coordinates of the vertex of the function below? Write the answer in the form (x,y)
y + 9 = -6(x - 2)^2

1: Which of the following are quadratic functions. There can be multiple right answers. Check all that apply.

Y= 5x - 3x^2

Y= x - x^3

Y= 2x^2 -3x + 7

Y= 3x -4
---------------------------------------...

2: Which of the following Quadratic functions has a graph that opens downward. There can be multiple right answers. Check all that apply.

Y= 3x^ - x - 1

Y= - (2x^2 - 1)

Y= 5/2 x - 3x^2

Y = 3/2 x^2 -3x +15
---------------------------------------...

3: In which form is the following function written

Y= -2(x - 3)(x+5)
---------------------------------------...

4: In which form is the following function written.

y-3 = 1/2 (x - 1)^2
---------------------------------------...

18: Assume f(x) = -2x + 8 and g(x) = 3x , what is the value of (g o f)(3)?

A: 6
B: x + 8
C: -10
D: 23

19: None

20: Let h(x) = (g o f)(x) = x^2/ x^2 + 1
Which of the following could be a possible decomposition of h(x)?

A: F(x) = x^2 ; g(x) = x
-------
x + 1

B: f(x) = x + 1; g(x) = x^2

C: f(x) = x + 1; g(x) = 1
-----
x^2

D: f(x) = x ;g(x) = x
-------
x + 1

14: Which of the following is the equation of the line perpendicular to the line y = -10x + 1 , passing through the point (5,7)?

A: 1 13
---- x – y = - ----
10 2


B: 1 13
--- x + y = - -----
10 2

Yes B and C are the same for some reason.

C: 1 13
--- x + y = - -----
10 2


1 13
D: - ------ x – y = --------
10 2

15: None

16: How many solutions does the following system of equations have?
Y = 5/2x + 2
2y=5x + 8

A: one
B: two
C: Zero
D: Infinitely many.

17: Assume f(x) = -2x + 8 and g(x) = 5x , what is the value of (f – g)(2)?
Answer: _______

12: Let y = 3t + 6 be a linear function representing the distance from home for an ant t minutes after starting out from a location near its home. What does the number 6 represent in this function?

A: The ant is 6 feet from its home after t minutes.
B: The ant started out 6 feet from its home.
C: The ant is moving at 6 feet per minute.
D: The ant is moving 6 feet every 3 minutes.

13: Which of the following is the equation of a line parallel to the line y = 4x + 1 , passing through the point (5,1)?

A: 4x + y = -19
B: 4x – y = 19
C: -4x – y =19
D: 4x + y =19

9: If you were to solve the following system of equations by using a matrix, which of the following would be your coefficient matrix?
5x – y = 18
3x + 8y =15

A: [5 18]
[3 15]

B: [5 -1 18]
[3 8 15]

C: [5 -1]
[3 8]

D: [5 3]
[-1 8]

10: It is possible for a system of linear equations to have an infinite number of solutions
A: True
B: False

11: Let y = 3t + 6 be a linear function representing the distance from home for an ant t minutes after starting out from a location near its home. What does the number 3 represent in this function.?

A: The ant is 3 feet from its home after t minutes.
B: The ant started out 3 feet from its home.
C: The ant is crawling at 3 feet per minute.
D: The ant is moving 3 feet every 6 minutes.

4: Which of the following is a true statement about functions.

A: If A and B are matrices, then AB = BA

B: If f and g are functions, then (f o g)(x) = (g o f)(x)

C: If f and g are functions, then (f + g)(x) = (g + f)(x)

D: If f is a function, then f(a + h) =f(a) +f(h)

5: None

6: Solve the system of equations below.
5x -2y = 18
3x +3y = 15

A: (1,4)
B: (-1,4)
C: (4,1)
D: (-4,1)

7: Find the sum of the first 50 terms of the sequence below.
An = 3n + 2
Answer: ______

8: If you save one penny on January 1, two pennies on January 2, three pennies on January 3, and continue this pattern for one year (not a leap year), what will be the value of your entire savings, in dollars at the end of that one year? Express your answer as a decimal.
Answer: _____

1: If f(x) = x^2 + 3x + 5 , what is f(3 + h)?

A: (3 + h)^2 + 8 + h

B: h^2 + 9h + 23

C: (x^2 +3x +5)(3 + h)

D: h^2 + h + 23

2: Which of the following is true about the function shown below?

1
-----
√x-6

A: Its domain is (6, ∞ ) and its range is (- ∞ , ∞)

B: Its domain is (6, ∞ ) and its range is (- ∞ ,0) U(0, ∞ )

C: Its domain is (6, ∞ ) and its range is (0, ∞ )

D: Its domain is (- ∞ , 0) and its range is (0, ∞ )

3: Which of the following statements are true regarding functions. There are multiple right answers. Check all that apply.

A function is a relation in which multiple values of the input variable are paired with at least one of the output variable

A sequence is a function whose domain is the set of rational numbers.

The vertical line test may be used to determine whether a relation is a function

The horizontal line test may be used to determine whether a function is one to one.