Relations and Functions

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x-value) and an output (y-value).

Front

What is a function?

Back

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

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 are the domain and range of a function?

Back

The domain is the set of all possible input values (x-values), and the range is the set of all possible output values (y-values).

Front

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

Back

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

Front

What is a linear function?

Back

A linear function is a function that can be represented by a straight line on a graph, typically in the form y = mx + b.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be represented by a parabola, typically in the form y = ax^2 + bx + c.

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 y = c.

Front

What is the difference between independent and dependent variables?

Back

The independent variable is the input of a function (x), while the dependent variable is the output (y) that depends on the input.

Front

What is a piecewise function?

Back

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