Domain and Range of Graphs

Front

What is the definition of the domain of a function?

Back

The domain of a function is the complete set of possible values of the independent variable (usually x) for which the function is defined.

Front

What is the definition of the range of a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that the function can output.

Front

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

Back

The domain can be determined by identifying all the x-values for which the graph has points. Any x-value that results in a point on the graph is included in the domain.

Front

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

Back

The range can be determined by identifying all the y-values that the graph reaches. Any y-value that corresponds to a point on the graph is included in the range.

Front

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

Back

A restricted domain means that not all possible x-values are included; certain values are excluded due to the nature of the function (e.g., division by zero, square roots of negative numbers).

Front

What is the notation for expressing the domain of a function?

Back

The domain can be expressed using interval notation, such as (a, b) for open intervals or [a, b] for closed intervals.

Front

What is the notation for expressing the range of a function?

Back

The range can also be expressed using interval notation, similar to the domain, indicating the set of y-values that the function can take.

Front

What is the vertical line test?

Back

The vertical line test is a method used to determine if a graph represents a function. If a vertical line intersects the graph at more than one point, the graph does not represent a function.

Front

What is an example of a function with a limited range?

Back

The function f(x) = x^2 has a range of [0, ∞) because it only outputs non-negative values.

Front

What is an example of a function with a limited domain?

Back

The function f(x) = 1/x has a domain of (-∞, 0) ∪ (0, ∞) because it is undefined at x = 0.