Functions

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a curve is a graph of a function. If any vertical line intersects the graph at more than one point, then the graph 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 does it mean for a function to be one-to-one?

Back

A function is one-to-one if it never assigns the same value to two different domain elements; in other words, each output is produced by exactly one input.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Front

What is a quadratic function?

Back

A quadratic function is a function that can be expressed in the form f(x) = ax² + bx + c, where a, b, and c are constants and a ≠ 0. Its graph is a parabola.

Front

What is a constant function?

Back

A constant function is a function that always returns the same value regardless of the input. It can be expressed 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 parts of its domain.

Front

What is an inverse function?

Back

An inverse function reverses the operation of the original function. If f(x) takes an input x to an output y, then the inverse function f⁻¹(y) takes y back to x.