Functions and Relations

Front

What is a function in mathematics?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

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 the graph is not a function.

Front

What is a relation in mathematics?

Back

A relation is a set of ordered pairs, where each pair consists of an input (x) and an output (y). A relation can be a function if it meets the criteria of having only one output for each input.

Front

How can you determine if a mapping is a function?

Back

To determine if a mapping is a function, check if each input (x-value) is associated with exactly one output (y-value). If any input has multiple outputs, it is not a function.

Front

What is the definition of a one-to-one function?

Back

A one-to-one function is a function where each output is associated with exactly one input. No two different inputs can produce the same output.

Front

What is the difference between a function and a non-function?

Back

A function has a unique output for every input, while a non-function may have one or more inputs that produce multiple outputs.

Front

What is a mapping diagram?

Back

A mapping diagram visually represents a function or relation by showing how each input is paired with its corresponding output.

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. It can be drawn without lifting the pencil from the paper.