Domain and Range FLASHCARD

Front

What is the definition of 'domain' in a relation?

Back

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

Front

What is the definition of 'range' in a relation?

Back

The range of a relation is the set of all possible output values (y-values) that result from the input values in the domain.

Front

How do you determine the domain from a graph?

Back

To determine the domain from a graph, identify the x-values that the graph covers, including any restrictions.

Front

How do you determine the range from a graph?

Back

To determine the range from a graph, identify the y-values that the graph covers, including any restrictions.

Front

What is the domain of the function f(x) = 1/(x-3)?

Back

The domain is all real numbers except x = 3, since the function is undefined at that point.

Front

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

Back

The range is all real numbers greater than or equal to 0, since x^2 cannot be negative.

Front

What does it mean if a function has a restricted domain?

Back

A restricted domain means that not all real numbers are valid inputs for the function, often due to limitations in the context of the problem.

Front

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

Back

The domain is all real numbers x such that x ≥ 0, since the square root of a negative number is not defined in the real number system.

Front

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

Back

The range is all real numbers, since as x takes on all real values, -x will also take on all real values.

Front

How can you express the domain of a function using interval notation?

Back

Interval notation uses brackets and parentheses to describe the set of x-values. For example, [a, b) means x is between a and b, including a but not b.