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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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.

Tags

CCSS.8.F.A.1

CCSS.HSF.IF.B.5

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).

Tags

CCSS.HSF-BF.B.4D

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, ∞).