Domain and Range of Graphs

Front

What is the definition of 'domain' in relation to graphs?

Back

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

Front

What is the definition of 'range' in relation to graphs?

Back

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

Front

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

Back

To determine the domain, identify the x-values that the graph covers. Look for any restrictions such as holes or vertical asymptotes.

Front

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

Back

To determine the range, identify the y-values that the graph covers. Look for any restrictions such as horizontal asymptotes or gaps.

Front

What does the notation (-3, 3) represent?

Back

The notation (-3, 3) represents an open interval where x can take any value greater than -3 and less than 3.

Front

What does the notation [-4, 5) represent?

Back

The notation [-4, 5) represents a closed interval at -4 and an open interval at 5, meaning x can take values from -4 to 5, including -4 but not including 5.

Front

What is the domain of the function f(x) = √(x + 4)?

Back

The domain is x ≥ -4, 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 square of any real number is non-negative.

Front

If a graph has a vertical asymptote at x = 2, what can be said about its domain?

Back

The domain will not include x = 2, as the function is undefined at that point.

Front

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

Back

The domain is all real numbers except x = 3, where the function is undefined.