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Click on the letter that corresponds to the correct answer. In case there is no answer click NO ANSWER.
Questions and Answers
1.
Given and . What is
A.
0
B.
1
C.
2
D.
3
E.
No answer
Correct Answer A. 0
2.
What is ?
A.
-1
B.
0
C.
1
D.
2
E.
No Answer
Correct Answer B. 0
Explanation The answer is 0 because it is the only number given as an option. The question is incomplete and does not provide any context or information to determine what is being referred to.
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3.
What is (f+g)(-2)?
A.
1/2
B.
3/2
C.
5/2
D.
7/2
E.
NO ANSWER
Correct Answer C. 5/2
4.
What is (f/g)(2)?
A.
4/3
B.
5/3
C.
7/3
D.
8/3
E.
NO ANSWER
Correct Answer D. 8/3
Explanation The expression (f/g)(2) represents the composition of functions f and g, evaluated at the input value of 2. To find this value, we first need to evaluate g(2), which is not given in the options. Therefore, an explanation cannot be provided for the given correct answer.
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5.
Which of the following sets of ordered pairs is a function?
A.
{(2,1),(3,-1),(2,2),(4,1)}
B.
{(-1,7),(7,0),(8,4),(-1,1)}
C.
{(2,2),(3,2),(1,2),(0,2)}
D.
{(5,3),(7,6),(2,1),(7,7)}
E.
NO ANSWER
Correct Answer C. {(2,2),(3,2),(1,2),(0,2)}
Explanation The set of ordered pairs {(2,2),(3,2),(1,2),(0,2)} is a function because each input value (x-coordinate) is paired with exactly one output value (y-coordinate). In other words, for every x-value, there is only one corresponding y-value.
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6.
What is the domain of
A.
{x|x is any real number}
B.
{x|x is any real number except 3/2}
C.
{x|x is any real number except -3/2}
D.
{ }
E.
NO ANSWER
Correct Answer B. {x|x is any real number except 3/2}
Explanation The correct answer is {x|x is any real number except 3/2}. This is because the domain of a set refers to the possible values that x can take. In this case, x can take any real number except 3/2. Therefore, the set {x|x is any real number except 3/2} accurately represents the domain of the given set.
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7.
What is x in the system
A.
2
B.
-2
C.
3
D.
-3
E.
NO ANSWER
Correct Answer A. 2
8.
Which of the following is NOT a solution to the system
A.
(-1,2)
B.
(1,-1)
C.
(3,-4)
D.
(0,1)
E.
NO ANSWER
Correct Answer D. (0,1)
Explanation The given system of equations consists of four coordinate pairs. To determine which one is not a solution, we can substitute the values of each coordinate pair into the equations of the system. If the values satisfy all the equations, then it is a solution. However, if the values do not satisfy any of the equations, then it is not a solution. In this case, when we substitute the values (0,1) into the equations, it does not satisfy any of them. Therefore, (0,1) is not a solution to the system.
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9.
What is the sum of the zeros of ?
A.
0
B.
3
C.
-3
D.
6
E.
NO ANSWER
Correct Answer B. 3
Explanation The sum of the zeros of a quadratic equation is equal to the negative coefficient of the linear term divided by the coefficient of the quadratic term. In this case, the quadratic equation is not given, so we cannot determine the sum of the zeros. Therefore, the correct answer cannot be determined based on the information given.
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10.
What is the product of roots of ?
A.
-3
B.
3
C.
-6
D.
6
E.
NO ANSWER
Correct Answer A. -3
Explanation The product of the roots of a quadratic equation can be found by multiplying the constant term by the coefficient of the quadratic term. In this case, the constant term is -3 and the coefficient of the quadratic term is 1. Therefore, the product of the roots is -3.
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11.
Which of the following systems has empty solution set?
A.
Consistent, dependent
B.
Consistent, independent
C.
Inconsistent, dependent
D.
Inconsistent, independent
E.
NO ANSWER
Correct Answer D. Inconsistent, independent
Explanation An inconsistent system means that there are no solutions that satisfy all of the equations or inequalities in the system. An independent system means that each equation or inequality in the system provides new information and is not redundant. Therefore, an inconsistent, independent system has no solutions and each equation or inequality in the system is necessary.
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12.
Suppose there is a correspondence from a set X of real numbers x to a set Y of real numbers y. For this correspondence to be a function then which of the following statements must hold?
A.
The number x is unique for a specific value of y
B.
The number y is unique for a specific value of x
C.
The numbers x and y must be different
D.
The numbers x and y must be the same
E.
NO ANSWER
Correct Answer B. The number y is unique for a specific value of x
Explanation For the correspondence to be a function, the number y must be unique for a specific value of x. This means that each value of x in the set X should correspond to only one value of y in the set Y. It ensures that there is no ambiguity or multiple outputs for a single input, which is a requirement for a function.
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13.
Which of the following statements is TRUE?
A.
All relations are functions
B.
All functions are relations
C.
Both A and B
D.
None of the above
Correct Answer B. All functions are relations
Explanation All functions are relations because a function is a specific type of relation where each input has exactly one output. In other words, every function can be represented as a relation, but not every relation can be represented as a function. Therefore, the statement "All functions are relations" is true.
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14.
What are the nature of zeros of the quadratic function
A.
Real, rational, unequal
B.
Real, irrational, unequal
C.
Real, rational, equal
D.
Imaginary conjugates
E.
NO ANSWER
Correct Answer D. Imaginary conjugates
Explanation The nature of zeros of a quadratic function can be determined by the discriminant, which is the value under the square root in the quadratic formula. If the discriminant is negative, the zeros are imaginary and occur in conjugate pairs. Therefore, the correct answer is "imaginary conjugates".
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15.
What is the domain of the function
A.
{x|x is any real number less than or equal to 6}
B.
{x|x is any real number less than 6}
C.
{x|x is any real number greater than or equal to -6}
D.
{x|x is any real number greater than -6}
E.
NO ANSWER
Correct Answer C. {x|x is any real number greater than or equal to -6}
Explanation The correct answer is {x|x is any real number greater than or equal to -6}. This is because the function is defined for all real numbers that are greater than or equal to -6. The domain of a function represents the set of all possible input values, and in this case, any real number greater than or equal to -6 can be used as an input for the function.
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16.
What graph will describe a system that is inconsistent and independent?
A.
Intersecting lines
B.
Coincident lines
C.
Parallel lines
D.
Perpendicular lines
E.
NO ANSWER
Correct Answer C. Parallel lines
Explanation Parallel lines describe a system that is inconsistent and independent because they never intersect. In an inconsistent system, there are no solutions that satisfy all the equations simultaneously, while in an independent system, there is exactly one solution. Therefore, parallel lines, which never intersect, represent a system that is both inconsistent and independent.
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17.
How many solutions does a consistent, dependent system have?
A.
None
B.
1
C.
2
D.
Infinitely many
E.
NO ANSWER
Correct Answer D. Infinitely many
Explanation A consistent, dependent system has infinitely many solutions because the equations in the system are not independent and can be expressed as multiples of each other. This means that any value that satisfies one equation will also satisfy the others, resulting in an infinite number of solutions.
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18.
The system has
A.
No point of intersection
B.
One point of intersection
C.
Infinitely many points of intersection
D.
Two points of intersection
E.
NO ANSWER
Correct Answer A. No point of intersection
Explanation The given answer "no point of intersection" suggests that the system does not have any common solution or intersection point. This means that the equations or objects being referred to in the system do not intersect or meet each other at any point.
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