Domain and Range

Front

What is the definition of Domain in mathematics?

Back

The set of all possible input values (x-values) for a function.

Front

What is the definition of Range in mathematics?

Back

The set of all possible output values (y-values) for a function.

Front

What does the vertical line test determine?

Back

It determines if a graph represents a function; if a vertical line intersects the graph at more than one point, it is not a function.

Front

If a function has a domain of -4 ≤ x ≤ 3, what does this mean?

Back

It means that the input values (x-values) can range from -4 to 3, inclusive.

Front

If a function has a range of -8 ≤ y ≤ 2, what does this mean?

Back

It means that the output values (y-values) can range from -8 to 2, inclusive.

Front

What is an example of a function that does not pass the vertical line test?

Back

A circle, as a vertical line can intersect it at two points.

Front

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

Back

The domain is x ≥ 1, since the expression under the square root must be non-negative.

Front

What is the range of the function f(x) = x^2?

Back

The range is y ≥ 0, since the output of a square function is always non-negative.

Front

How do you find the range of a linear function?

Back

The range of a linear function is all real numbers unless restricted by the context.

Front

What is the domain of the function f(x) = 1/(x-2)?

Back

The domain is all real numbers except x = 2, where the function is undefined.