Domain, Range, & End Behavior

Front

What is the definition of Domain in mathematics?

Back

The set of all possible input values (x-values) for a function.

Front

What is the definition of Range in mathematics?

Back

The set of all possible output values (y-values) for a function.

Front

What does End Behavior refer to in a function?

Back

The behavior of the graph of a function as x approaches positive or negative infinity.

Front

How do you determine the Domain of a function graphically?

Back

Identify the x-values for which the function is defined; look for any breaks or restrictions in the graph.

Front

How do you determine the Range of a function graphically?

Back

Identify the y-values that the function can take; observe the highest and lowest points on the graph.

Front

What is the Domain of the function f(x) = √(x-4)?

Back

[4, ∞) because the expression under the square root must be non-negative.

Front

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

Back

[0, ∞) because the output of x^2 is always non-negative.

Front

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

Back

As x → ∞, f(x) → ∞; as x → -∞, f(x) → ∞.

Front

What is the End Behavior of the function f(x) = -x^2?

Back

As x → ∞, f(x) → -∞; as x → -∞, f(x) → -∞.

Front

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

Back

(-∞, 3) U (3, ∞) because x cannot equal 3.