Exploring Relations and Functions

What is the definition of a relation in mathematics?

• A relation is a function that maps every element of one set to a unique element of another set.

• A relation is a collection of unordered elements from multiple sets.

• 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.

How can you determine if a relation is a function?

• A relation is a function if it has multiple outputs for the same input.

• A relation is a function if it has no inputs at all.

• A relation is a function if each output can correspond to multiple inputs.

• A relation is a function if each input has exactly one output.

Given the set of ordered pairs {(1, 2), (2, 3), (1, 4)}, is this relation a function?

• No, this relation is not a function.

• The relation is a function because it has three pairs.

• Yes, this relation is a function.

• This relation has unique outputs for each input.

Graph the function f(x) = 2x + 3. What is its slope?

• 1

• 3

• 2

• -2

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

• All real numbers except 0

• All real numbers

• All real numbers except 2

• Only positive numbers

Identify the range of the function f(x) = x^2 - 4.

• [0, 4]

• [-4, ∞)

• (-4, 0)

• (-∞, -4)

How do you find the x-intercept of a function?

• Set the function f(x) = 1 and solve for x.

• Find the derivative of the function and set it to zero.

• Evaluate the function at x = 0.

• Set the function f(x) = 0 and solve for x.

What is the vertical line test and how is it used?

• The vertical line test determines the slope of a graph.

• The vertical line test is used to determine if a graph represents a function.

• The vertical line test is a method for calculating the distance between points.

• The vertical line test is used to find the area under a curve.

Given the function f(x) = √(x - 1), what is its domain?

• (0, 1)

• (1, 2)

• (-∞, 1)

• [1, ∞)

Graph the relation defined by the equation y = |x|. What is its shape?

• The shape is a circle.

• The shape is a V.

• The shape is a parabola.

• The shape is a straight line.