Domain and Range of Graphs

Front

What is the domain of a graph?

Back

The set of all possible input values (x-values) for which the function is defined.

Front

What is the range of a graph?

Back

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

Front

What does it mean if a graph has a domain of all real numbers?

Back

It means that the function can accept any real number as an input.

Front

How do you determine the domain of a function from its graph?

Back

Look for the x-values that the graph covers; any x-value that the graph does not touch is not included in the domain.

Front

What is the notation for an open interval?

Back

An open interval is denoted by parentheses, e.g., (a, b) means a < x < b.

Front

What is the notation for a closed interval?

Back

A closed interval is denoted by brackets, e.g., [a, b] means a ≤ x ≤ b.

Front

What does the notation (-∞, ∞) represent?

Back

It represents all real numbers, indicating that there are no restrictions on the domain.

Front

If a graph has a range of [-2, ∞), what does this mean?

Back

The output values (y-values) start from -2 and go up to positive infinity, including -2 but not including infinity.

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

How can you find the domain of a rational function?

Back

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