Relations and Functions

Front

What is a function?

Back

A relation where every input (x-value) has exactly one output (y-value).

Front

What is the vertical line test?

Back

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

Is the relation {(1,2), (2,3), (3,4)} a function?

Back

Yes, because each input has a unique output.

Front

Is the relation {(1,2), (1,3), (2,4)} a function?

Back

No, because the input '1' has two different outputs (2 and 3).

Front

What are ordered pairs?

Back

A pair of numbers (x, y) that represent a point in a coordinate system.

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

Give an example of a linear function.

Back

f(x) = 2x + 3 is a linear function.

Front

What is a relation?

Back

A set of ordered pairs, which can include functions but is not limited to them.

Front

What does it mean for a function to be one-to-one?

Back

Each output is paired with exactly one input, meaning no two different inputs produce the same output.