Algebra Answers

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
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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
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3: In which form is the following function written

Y= -2(x - 3)(x+5)
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4: In which form is the following function written.

y-3 = 1/2 (x - 1)^2
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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
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During a research experiment, it was found that the number of bacteria in a culture grew at a rate proportional to its size. At 100:00 AM there were 5,00 bacteria present in the culture. At noon, the number of bacteria grew to 5,800. How many bacteria will there be at midnight?

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


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



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: _______

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.

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

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: _____

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

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)

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: ______

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.

The numerator of a fraction is one less than its denominator. If 3 is added to each of its numerator and denominator then the fraction is increased by 3/28. Find the fraction

1: State the degree:
x^5 y^2 +7x^3 y^7 -3x^2 y^4
Answer: ____

2: The function f(x) = x + pie is a polynomial.
A: True
B: False

3: What is the leading coefficient of this polynomial when written in standard form?

1 – 2x +5x^4

Answer: _____

4: Which polynomial is a monomial?

A: 5r^2 s^3 t^4
B: 1 – 2x + 5x^4
C: 6 – 2x^3 -4x^2 + x^5
D: 2p^2 – p


5: State the degree

-4a^3 b^2 c^5

Answer: ____