WorksheetsUnderstanding Relations and Functions
Total questions: 10
Worksheet time: 5mins
What is the definition of a relation in mathematics?
A relation is a collection of unordered elements without any specific pairing.
A relation is a single pair of elements from two sets.
A relation is a set of ordered pairs that defines a relationship between elements of two sets.
A relation is a function that maps every element of one set to a unique element of another set.
How can you determine if a relation is a function?
A relation is a function if each input has exactly one output.
A relation is a function if it has multiple outputs for the same input.
A relation is a function if it includes at least one input-output pair.
A relation is a function if it is represented by a straight line on a graph.
Given the set of ordered pairs {(1, 2), (2, 3), (1, 4)}, is this relation a function? Why or why not?
No, this relation is a function because it has multiple outputs for one input.
No, this relation is not a function.
This relation is a function since it has only one output for each input.
Yes, this relation is a function because all inputs are unique.
Identify the domain of the function f(x) = 2x + 3.
Only positive numbers
Only negative numbers
Integers between 1 and 10
All real numbers
Identify the range of the function f(x) = x^2.
(-∞, 0)
[0, ∞)
(0, 1)
[1, 2]
What is the domain of the relation represented by the set of points {(3, 5), (4, 6), (5, 7)}?
{2, 4, 5}
{3, 4, 5}
{3, 4, 6}
{1, 2, 3, 4, 5}
If a function is defined as f(x) = 1/(x-2), what is the domain?
All real numbers
All real numbers except x = 2
x < 2
x = 2 only
Explain how to find the range of the function f(x) = -x^2 + 4.
(-∞, 4]
(4, ∞)
[0, 4]
(-∞, 0)
Given the function g(x) = √(x-1), what is the domain?
(−∞, 1)
(1, 2)
[0, 1]
[1, ∞)
Is the relation defined by the equation y = 2x + 1 a function? Explain your reasoning.
No, it is a function but it has no real solutions.
Yes, it is a function but only for positive values of x.
No, it is not a function because it does not pass the vertical line test.
Yes, it is a function.
