Question

what is the domain of the function shown in the graph below?

Explanation:

Step1: Identify domain definition

The domain of a function is the set of all valid $x$-values for which the function is defined, corresponding to the horizontal span of its graph.

Step2: Locate graph's x-extents

The graph starts at $x=-6$ (closed dot, included) and ends at $x=1$ (closed dot, included), with all $x$-values in between covered.

Step3: Write domain in interval form

The set of $x$-values is all real numbers from $-6$ to $1$, inclusive.

Answer:

$-6 \leq x \leq 1$ (or in interval notation: $[-6, 1]$)