Understanding Functions and Their Properties

Front

What is a function?

Back

A function is a relation where every input (x-value) has exactly one output (y-value).

Front

How can you determine if a relation is a function?

Back

You can determine if a relation is a function by using the vertical line test: if a vertical line intersects the graph at more than one point, it is not a function.

Front

What does the vertical line test indicate?

Back

The vertical line test indicates whether a graph represents a function. If any vertical line crosses the graph more than once, the relation is not a function.

Front

What is an input in a function?

Back

An input is the value you provide to a function, typically represented as 'x'.

Front

What is an output in a function?

Back

An output is the value that results from applying the function to an input, typically represented as 'y'.

Front

Can a function have the same output for different inputs?

Back

Yes, a function can have the same output for different inputs, but each input must have only one output.

Front

What is a relation?

Back

A relation is a set of ordered pairs, where each pair consists of an input and an output.

Front

Give an example of a function.

Back

An example of a function is f(x) = 2x + 3, where for each x-value, there is one corresponding y-value.

Front

What is a non-function?

Back

A non-function is a relation where at least one input is associated with more than one output.

Front

What happens if a vertical line crosses a graph at two points?

Back

If a vertical line crosses a graph at two points, the relation is not a function.