Functions

Front

What is a function?

Back

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

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How do you determine if a relation is a function?

Back

A relation is a function if each input value corresponds to exactly one output value. This can be checked using the vertical line test on a graph.

Front

What is the vertical line test?

Back

The vertical line test states that if a vertical line intersects a graph at more than one point, then the graph does not represent a function.

Front

What is an independent variable?

Back

An independent variable is the input value (x-value) in a function, which can be freely chosen.

Front

What is a dependent variable?

Back

A dependent variable is the output value (y-value) in a function, which depends on the input value.

Front

What is the difference between domain and range?

Back

Domain refers to the set of input values, while range refers to the set of output values of a function.

Front

What does it mean for a function to be continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each output value is paired with exactly one input value, meaning no two different inputs produce the same output.