Relations and Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y).

Front

What is a function?

Back

A function is a special type of relation where each input has exactly one output.

Front

List the ordered pairs for the function f(x) = 2x + 1 for x = 0, 1, 2, 3.

Back

(0, 1), (1, 3), (2, 5), (3, 7)

Front

What does it mean for a relation to be a function?

Back

It means that for every input value, there is one and only one output value.

Front

How can you determine if a relation is a function using a graph?

Back

Use the vertical line test: if a vertical line intersects the graph at more than one point, the relation is not a function.

Front

What are ordered pairs?

Back

Ordered pairs are pairs of numbers written in the form (x, y), where x is the input and y is the output.

Front

What is the domain of a function?

Back

The domain is the set of all possible input values (x) for the function.

Front

What is the range of a function?

Back

The range is the set of all possible output values (y) that the function can produce.

Front

Give an example of a function and its domain and range.

Back

Example: f(x) = x^2; Domain: all real numbers; Range: all non-negative real numbers.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form f(x) = mx + b.