Question

Please describe the domain and range of the function shown in the following graph. You may use whichever form of notation you prefer- inequality, interval, or set notation.

Answer 1

• Domain (-∞, ∞)
• Range [0, ∞)

Step-by-step explanation

The domain is the set of allowed x inputs. The parabola stretches forever to the left and right. There aren't any restrictions to worry about, so we conclude the domain is "the set of all real numbers".

As an inequality, the domain would be -∞ < x < ∞ and then that condenses to the interval notation (-∞, ∞)

The range would be the interval notation [0, ∞)

The square bracket is to include the endpoint y = 0. The range written in inequality form is y ≥ 0. This is the set of nonnegative real numbers.