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 graph represents a function. If any vertical line intersects the graph at more than one point, then it is not a function.

Front

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

Back

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

Front

What is a domain in a function?

Back

The domain of a function is the complete set of possible values of the independent variable (input) for which the function is defined.

Front

What is a range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (output) that the function can produce.

Front

Can a function have multiple outputs for a single input?

Back

No, a function cannot have multiple outputs for a single input. Each input must correspond to exactly one output.

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line and can be expressed in the form y = 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 y = ax² + bx + c, where a, b, and c are constants and a ≠ 0.

Front

What is the difference between a function and a relation?

Back

A relation is a set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

What is an independent variable?

Back

An independent variable is a variable that represents the input of a function, which can be freely chosen.