Question

determine the domain of the function graphed below. options: (-1, 9), -1, 4, -1, 9, (-1, 4)

Explanation:

Step1: Understand Domain Definition

The domain of a function is the set of all x - values for which the function is defined. For a graphed function, we look at the horizontal extent of the graph (the left - most and right - most x - values that the graph covers).

Step2: Identify Left - Most and Right - Most x - Values

Looking at the graph, the left - most point (the point with the smallest x - value) has an x - coordinate of - 1 (since it is a closed dot, this value is included in the domain). The right - most point (the point with the largest x - value) has an x - coordinate of 9 (also a closed dot, so this value is included in the domain).

Step3: Determine the Domain Interval

Since the domain includes all x - values from - 1 to 9 (inclusive), the domain is written in interval notation as \([-1,9]\).

Answer:

\([-1, 9]\) (corresponding to the option \([-1, 9]\))