Understanding Relations and Functions

What is a relation in mathematics?

• A relation is a set of ordered pairs that defines a relationship between two sets.

• A relation is a single pair of numbers.

• A relation is a function that maps one set to another.

• A relation is a geometric shape defined by points in space.

Define a function in your own words.

• A function is a type of variable that stores data.

• A function is a single line of code that performs a task.

• A function is a method to create user interfaces.

• A function is a reusable block of code that takes inputs and returns an output.

What is the domain of a function?

• The graphical representation of a function.

• The range of a function.

• The set of all possible input values for a function.

• The constant value of a function.

What is the range of a function?

• The set of all possible input values of a function.

• The maximum value a function can achieve.

• The set of all possible output values of a function.

• The average value of a function over its domain.

How can you identify 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 every output is related to at least one input.

• A relation is a function if it contains no repeated inputs.

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

Differentiate between a relation and a function.

• A function can have no outputs for an input, while a relation must have at least one output.

• A relation is always a subset of a function, and functions cannot be relations.

• A relation must have one output for each input, while a function can have multiple outputs.

• A relation can have multiple outputs for a single input, while a function has exactly one output for each input.

Evaluate the function f(x) = 2x + 3 for x = 4.

• 10

• 7

• 15

• 11

What is the output of the function g(x) = x^2 when x = -2?

• 0

• 2

• -4

• 4

Graph the linear function y = 3x - 1.

• The graph is a horizontal line passing through (0, -1).

• The graph of the linear function y = 3x - 1 is a parabola opening upwards.

• The graph of the linear function y = 3x - 1 is a straight line with a slope of 3 and a y-intercept at (0, -1).

• The slope of the line is -3 and the y-intercept is (0, 1).

What does function notation f(x) represent?

• A function named 'f' evaluated at the input 'x'.

• The output of a function 'f' when no input is provided.

• A variable 'f' that holds the value of 'x'.

• A notation used for defining constants in mathematics.