Functions, Functions, Functions

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input from a given set.

Front

How can you determine if a table represents a function?

Back

A table represents a function if each input (x-value) is associated with exactly one output (y-value). If any x-value is repeated with different y-values, it is not a function.

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If any vertical line intersects the curve more than once, the curve is not a function.

Front

What does it mean for a mapping to be a function?

Back

A mapping is a function if every element in the domain is paired with exactly one element in the codomain.

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

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 one-to-one function?

Back

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

Front

What is a linear function?

Back

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