Question Bank: Relations and Functions

What is the Cartesian product of sets A = {1, 2} and B = {x, y}?

If set A = {a, b} and set B = {1, 2, 3}, how many ordered pairs can be formed?

Which of the following defines a relation?

What is the total number of ordered pairs formed by A × B if A = {x, y} and B = {1, 2, 3, 4}?

Which of the following is a valid ordered pair?

If P and Q are two sets, what is P × Q when P = {a} and Q = {}?

If set A has 5 elements and set B has 2 elements, how many ordered pairs can you form?

Identify a common misconception about Cartesian products.

If set A = {1, 2, 3} and set B = {x, y}, what is A × B?

Which of these represents a function from set A to set B?

Which of the following pairs is NOT a valid representation of a Cartesian product?

If A = {red, blue} and B = {circle, square}, what is A × B?

Which characteristic does an ordered pair need to have?

If A = {1, 2} and B = {x, y}, what is A × B?

How many elements are present in the Cartesian product of A = {a, b} and B = {1, 2, 3}?

Which of the following is true about the Cartesian product A × B?

If A = {1, 2, 3} and B = {x, y}, find a specific element of A × B.

For sets A = {a, b} and B = {1, 2}, which of these pairs is NOT in A × B?

Calculate the Cartesian product of B = {1, 2} and A = {a, b, c}. How many pairs will it have?

If P = {x, y, z} and Q = {1, 2}, what is P × Q?

What is the Cartesian product of two empty sets?

Determine the number of pairs in the Cartesian product C = {red, blue} × D = {circle, square, triangle}.

How many elements will the Cartesian product of A = {a, b, c, d} and B = {2, 3} contain?

If E = {x, y} and F = {1, 2, 3, 4}, which of the following represents an element of E × F?

Which statement about the order of elements in ordered pairs is correct?

If A has 4 elements and B has 5 elements, what is the number of pairs in A × B?

Link the situation: if A = {p, q} and B = {r}, how many unique pairs can be formed in A × B?

Given two sets A = {x} and B = {y, z}, what is A × B?

Which of the following is a relation from R to R?

What is the domain of the function f(x) = 1/(x - 2)?

Which of the following is a property of a reflexive relation?

What is the range of the function f(x) = x^2?

If R = {(x, y) : y = 2x + 1}, which of the following points belongs to R?

What type of function is defined by f(x) = |x|?

The relation R = {(a, b) : a - b ∈ Z} is what type of relation?

If two relations R and S are equal, which of the following must always be true?

Find the domain of the function f(x) = √(x - 4).

The graph of f(x) = x^3 is what type of function?

What is the effect of composing two functions f(g(x))?

Which of the following defines a polynomial function?

If f(x) = x^2 and g(x) = 3x + 4, what is (f + g)(x)?

The signum function f(x) gives which of the following outputs?

If R is a relation and it is transitive, which must hold?

What is the definition of an identity function?

Which of the following is true about a constant function?

What is the range of the function f(x) = |x|?

If f(x) = x^2 and g(x) = x + 1, what is (f - g)(x)?

What is the signum function f(x) defined as?

Which operation is used to combine functions f and g where (f g)(x) = f(x)g(x)?

If f(x) = kx, where k is a scalar, what is the form of αf?

Which of the following statements is false regarding the range of a constant function?

For which function is the graph always above the x-axis?

What is the effect of taking the modulus of a negative number?

Find (f + g)(x) if f(x) = 3x and g(x) = -2x.

What is (f / g)(x) for f(x) = x^2 and g(x) = x if g(x) ≠ 0?

Which function's graph passes through the origin and has a slope of 1?

Which operation involves evaluating two functions at the same input and finding their product?

In the modulus function, f(x) = |x|, what happens to negative values of x?

What is the graphical representation of a constant function?