Relations, Functions, Domain and Range

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 graph represents a function. If a vertical line intersects the graph at more than one point, it is not a function.

Front

What is the domain of 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 range of a function?

Back

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

Front

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

Back

No, because the x-value 1 has two different y-values (2 and 4).

Front

Is the relation {(3, 5), (4, 6), (5, 7)} a function?

Back

Yes, because each x-value has only one corresponding y-value.

Front

What does it mean if a graph does not pass the vertical line test?

Back

It means that the graph does not represent a function, as at least one x-value is associated with multiple y-values.

Front

If a function has a domain of {1, 2, 3}, what are the possible x-values?

Back

The possible x-values are 1, 2, and 3.

Front

If a function has a range of {4, 5, 6}, what are the possible y-values?

Back

The possible y-values are 4, 5, and 6.

Front

What is an example of a function?

Back

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