Function or Not a Function

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What is the definition of a relation?

Back

A relation is a set of ordered pairs, typically represented as (x, y).

Front

What is the Vertical Line Test?

Back

The Vertical Line Test is a method to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the Horizontal Line Test?

Back

The Horizontal Line Test checks if a function is one-to-one. If a horizontal line intersects the graph more than once, the function is not one-to-one.

Front

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

Back

For a relation to be a function, each input must correspond to exactly one output.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is an example of a function?

Back

An example of a function is f(x) = x^2, where each x-value has one corresponding y-value.

Front

What is an example of a relation that is not a function?

Back

An example of a relation that is not a function is {(1, 2), (1, 3)}, where the input 1 has two different outputs.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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