Identifying Functions

Front

What is a function in mathematics?

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 function. If a vertical line intersects the curve at more than one point, then the curve is not a function.

Front

What is the definition of 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 the difference between a function and a relation?

Back

A function is a specific type of relation where each input is associated with exactly one output, while a relation can have multiple outputs for a single input.

Front

What is a domain in the context of functions?

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 a range in the context of functions?

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 continuous?

Back

A function is continuous if there are no breaks, jumps, or holes in its graph, meaning it can be drawn without lifting the pencil from the paper.

Front

What is an example of a function that is not a one-to-one function?

Back

The function f(x) = x^2 is not one-to-one because both f(2) and f(-2) yield the same output (4).

Front

What is an example of a one-to-one function?

Back

The function f(x) = 2x + 3 is a one-to-one function because each input produces a unique output.

Front

What is a composite function?

Back

A composite function is formed when one function is applied to the result of another function, denoted as (f ∘ g)(x) = f(g(x)).