Functions

Front

What is the vertical line test and what does it determine?

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, the graph does not represent a function.

Front

Define a function in mathematical terms.

Back

A function is a relation that assigns exactly one output (y) for each input (x).

Front

What is the domain of a function?

Back

The domain of a function is the set of all possible input values (x) 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) that the function can produce.

Front

How do you evaluate a function at a specific point?

Back

To evaluate a function at a specific point, substitute the input value into the function's equation and simplify to find the output.

Front

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

Back

A mapping is a function if each input is associated with exactly one output.

Front

What is an example of a relation that is not a function?

Back

A relation where an input is associated with multiple outputs, such as {(1, 2), (1, 3)}, is not a function.

Front

What is the significance of the notation f(x)?

Back

The notation f(x) represents the output of the function f for the input x.

Front

What is a one-to-one function?

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 the difference between a function and a relation?

Back

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