Domain & Range (from graphs, functions, and applications)

Front

What is the domain of a function?

Back

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

Front

What is the range of a function?

Back

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

Front

How do you determine the domain from a graph?

Back

To determine the domain from a graph, identify the x-values for which the graph exists. Look for any breaks, holes, or vertical asymptotes.

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 reaches. Look for the highest and lowest points on the graph.

Front

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

Back

The domain is all real numbers except x = 0, or in interval notation: (-∞, 0) ∪ (0, ∞).

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, or in interval notation: [0, ∞).

Front

What is a reasonable domain for a function representing the height of a ball thrown in the air?

Back

The reasonable domain is the set of all real numbers greater than or equal to 0, as time cannot be negative.

Front

What is a reasonable range for a function representing the height of a ball thrown in the air?

Back

The reasonable range is all real numbers greater than or equal to 0, as height cannot be negative.

Front

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

Back

A restricted domain means that certain input values are not allowed, often due to the nature of the function (e.g., square roots, logarithms).

Front

What is the domain of the function f(x) = √(x - 2)?

Back

The domain is all real numbers greater than or equal to 2, or in interval notation: [2, ∞).