Functions

Front

What is a function?

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 y-value.

Front

What is the definition of 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 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

How can you determine if a relation is a function using the vertical line test?

Back

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

Front

Is the relation {(1,2), (1,3), (2,4)} a function?

Back

No, it is not a function because the input '1' corresponds to two different outputs (2 and 3).

Front

Is the relation {(0,1), (1,-3), (2,-4), (-4,1)} a function?

Back

Yes, it is a function because each input has exactly one output.

Front

What does it mean for a graph to represent a function?

Back

A graph represents a function if every x-value has only one corresponding y-value.

Front

What is an example of a function?

Back

An example of a function is f(x) = 2x + 3, where for each x-value, there is 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 y^2 = x, because for some x-values, there are two corresponding y-values.

Front

What is the domain of the function f(x) = 1/x?

Back

The domain is all real numbers except x = 0, since division by zero is undefined.