Domain and Range of Graphs

Front

What is the definition of 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 definition of 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 express the range of a function in interval notation?

Back

In interval notation, the range is expressed using brackets [ ] for closed intervals and parentheses ( ) for open intervals.

Front

What does it mean if a range is expressed as [1, ∞)?

Back

It means that the range includes all values from 1 to positive infinity, with 1 being included in the range.

Front

What does it mean if a domain is expressed as (-∞, ∞)?

Back

It means that the domain includes all real numbers, from negative infinity to positive infinity.

Front

What is the significance of parentheses in interval notation?

Back

Parentheses indicate that the endpoint is not included in the interval.

Front

What is the significance of brackets in interval notation?

Back

Brackets indicate that the endpoint is included in the interval.

Front

How would you express the domain of a function that includes all real numbers except for x = 3?

Back

The domain can be expressed as (-∞, 3) ∪ (3, ∞).

Front

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

Back

The domain is [1, ∞) because the expression under the square root must be non-negative.

Front

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

Back

The range is [0, ∞) because the output values are always non-negative.