Functions and Their Properties

Front

What is a function?

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

How can you determine if a set of ordered pairs is a function?

Back

A set of ordered pairs is a function if no two pairs have the same first element (x-value).

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

The range is the set of all possible output values (y-values) for a function.

Front

Given the function f(x) = 2x + 3, what is f(4)?

Back

f(4) = 2(4) + 3 = 11.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if any vertical line drawn through the graph intersects it at most once (Vertical Line Test).

Front

Is the set of ordered pairs {(1, 2), (2, 3), (1, 4)} a function?

Back

No, it is not a function because the input '1' is associated with two different outputs (2 and 4).

Front

What is the output of the function f(x) = x^2 when x = 5?

Back

f(5) = 5^2 = 25.

Front

If f(x) = 3x - 1, what is f(0)?

Back

f(0) = 3(0) - 1 = -1.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output.