Domain, Range and End Behavior

Front

What is the definition of Domain in 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 Range in a function?

Back

The range of a function is the complete set of possible values of the dependent variable (usually y) that result from using the function.

Front

How do you find the domain of a function?

Back

To find the domain, identify all the values of x that can be input into the function without causing any undefined situations, such as division by zero or taking the square root of a negative number.

Front

How do you find the range of a function?

Back

To find the range, determine all the possible output values (y) that the function can produce based on its domain.

Front

What is End Behavior in the context of functions?

Back

End behavior describes how the values of a function behave as the input values approach positive or negative infinity.

Front

What does it mean if a function's end behavior is 'As x → +∞, f(x) → -∞'?

Back

It means that as x increases without bound, the function's output values decrease without bound.

Front

What does it mean if a function's end behavior is 'As x → -∞, f(x) → +∞'?

Back

It means that as x decreases without bound, the function's output values increase without bound.

Front

What is the significance of identifying the range of a function?

Back

Identifying the range helps understand the possible outputs of a function and is crucial for graphing and solving equations.

Front

What is the significance of identifying the domain of a function?

Back

Identifying the domain is essential for understanding the valid inputs for a function and avoiding undefined values.

Front

How can you represent the domain of a function using interval notation?

Back

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