Domain and Range

Front

What is the definition of Domain in a function?

Back

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

Front

What is the definition of Range in a function?

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

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

The output values (y-values) can range from -8 to 2, inclusive.

Front

What is the relationship between domain and range?

Back

The domain consists of input values, while the range consists of output values derived from those inputs.

Front

What is an example of a function that does not have a defined range?

Back

A function that outputs all real numbers, such as f(x) = x, has a range of all real numbers.

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 squared number is always non-negative.

Front

How do you find the domain of a rational function?

Back

Identify values that make the denominator zero; these values are excluded from the domain.