Functions

Front

What is a function?

Back

A function is a relation where every input has exactly one output.

Front

What is the definition of a linear function?

Back

A linear function is a function that graphs to a straight line, which can be expressed in the form y = mx + b.

Front

What is the definition of a nonlinear function?

Back

A nonlinear function is a function that does not graph to a straight line and can include curves, parabolas, etc.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input (x-value) corresponds to exactly one output (y-value).

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 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

What is a one-to-one function?

Back

A one-to-one function is a function where each output is produced by exactly one input, meaning no two different inputs have the same output.

Front

What is a constant function?

Back

A constant function is a function that always returns the same value regardless of the input, represented as f(x) = c, where c is a constant.

Front

What is a piecewise function?

Back

A piecewise function is a function that is defined by different expressions for different intervals of the input.