Identifying Functions

Front

What is a function?

Back

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

Front

What is the vertical line test?

Back

The vertical line test is a method to determine if a curve is a function. If a vertical line intersects the curve at more than one point, it is not a function.

Front

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

Back

A relation is a function if every x-value is paired with only one y-value.

Front

Can a function have the same y-value for different x-values?

Back

Yes, a function can have the same y-value for different x-values, as long as each x-value has only one corresponding y-value.

Front

What is an example of a function?

Back

An example of a function is the equation y = 2x + 3, where each x-value gives a unique y-value.

Front

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

Back

An example of a relation that is not a function is the set of points {(1, 2), (1, 3)}, where the x-value 1 has two different y-values.

Front

What is the definition of a domain in a function?

Back

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

Front

What is the definition of a range in a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

What is a one-to-one function?

Back

A one-to-one function is a function where each x-value corresponds to a unique y-value, and each y-value corresponds to a unique x-value.

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.