Question

q# 17. what is the domain of the function shown in the graph below? (options: 1. $-8 \leq x \leq 8$; 2. $x \leq 8$; 3. $-8 \leq x < 8$; 4. $-8 \leq x < 8$)

Explanation:

Step1: Understand Domain Definition

The domain of a function is the set of all possible \( x \)-values for which the function is defined (i.e., the horizontal extent of the graph).

Step2: Analyze the Graph's Horizontal Range

Looking at the graph, the leftmost point (on the \( x \)-axis) seems to be at \( x = -3 \) (closed dot, so included) and the rightmost point is at \( x = 3 \) (closed dot, so included)? Wait, no, looking at the options, let's re - check. Wait, the graph: the left end is at \( x=-3 \) (closed circle) and the right end is at \( x = 3 \) (closed circle)? Wait, no, the options have \(-3\leq x\leq3\), \(x < 3\), \(3\leq x < 3\) (which is impossible), \(-3\leq x < 3\). Wait, maybe the leftmost \( x \)-value is \(-3\) (included, closed dot) and the rightmost \( x \)-value is \( 3 \) (included? Wait, no, maybe the right end is an open dot? Wait, no, let's look at the options. The first option is \(-3\leq x\leq3\), the fourth is \(-3\leq x < 3\). Wait, maybe the leftmost \( x \) is \(-3\) (closed) and the rightmost \( x \) is \( 3 \) (closed)? Wait, no, maybe I misread. Wait, the graph: let's see the \( x \)-axis. The left point is at \( x=-3 \) (closed) and the right point is at \( x = 3 \) (closed)? But the fourth option is \(-3\leq x < 3\). Wait, maybe the right end is an open dot. Wait, no, the first option is \(-3\leq x\leq3\). Wait, let's check the graph again. If the leftmost \( x \) is \(-3\) (included) and the rightmost \( x \) is \( 3 \) (included), then the domain is \(-3\leq x\leq3\). But wait, maybe the right end is at \( x = 3 \) with a closed dot? Wait, the first option is \(-3\leq x\leq3\), which would be the case if both ends are closed.

Wait, maybe I made a mistake. Let's re - examine the graph. The function's graph starts at \( x=-3 \) (closed circle) and ends at \( x = 3 \) (closed circle)? Or maybe the right end is open. Wait, the options: the first option is \(-3\leq x\leq3\), the fourth is \(-3\leq x < 3\). Wait, maybe the leftmost \( x \) is \(-3\) (included) and the rightmost \( x \) is \( 3 \) (included). So the domain is all \( x \) such that \(-3\leq x\leq3\).

Answer:

\(\boldsymbol{-3\leq x\leq3}\) (the first option, assuming the first option is labeled as, e.g., Option A: \(-3\leq x\leq3\))