Question

what is the domain of this function?
{ x | x ≥ 3 }
{ x | x ≥ 0 }
{ x | x > 0 }

Explanation:

Step1: Understand Domain Definition

Domain is all possible \( x \)-values of a function. For a graph, we look at the horizontal extent (leftmost to rightmost \( x \)-coordinates).

Step2: Analyze the Graph's Horizontal Extent

The graph (a V - shape) has its left end at \( x=-10 \) (arrow) and right end? Wait, no—wait the graph: left arrow is at \( x=-10 \), the vertex is at \( x=-7 \) (wait, grid: from -10, -8, -6... Wait, the leftmost point (arrow) is at \( x=-10 \), and the rightmost? Wait, no, maybe I misread. Wait, the graph is a V - shaped graph (absolute - value - like) with left arrow at \( x=-10 \) (left end) and right arrow? Wait, no, the original problem's options: Wait, no, maybe the user made a typo? Wait, no, the options given are \( \{x|x\geq3\} \), \( \{x|x\geq0\} \), \( \{x|x > 0\} \). Wait, maybe I misread the graph. Wait, no—wait, maybe the graph is actually a different one? Wait, no, the user's graph: the \( x \)-axis has -10, -8, -6, -4, -2, 0, 2,... But the options are about \( x\geq3 \), \( x\geq0 \), \( x > 0 \). Wait, maybe there's a mistake, but assuming the graph is a function where the domain starts at \( x = 0 \) or above. Wait, no—wait, maybe the graph is a function like \( y = |x - a|+b \) but the options are about \( x\geq0 \). Wait, the correct domain: if the graph is defined for all \( x\geq0 \), then the domain is \( \{x|x\geq0\} \). Wait, the middle option is \( \{x|x\geq0\} \). Let's re - evaluate:

Wait, the domain is the set of all \( x \)-values the graph covers. If the graph starts at \( x = 0 \) (or to the right) and goes to the right, then the domain is \( x\geq0 \). So the correct option is \( \{x|x\geq0\} \).

Answer:

\(\{x|x\geq0\}\) (assuming the graph's domain is all real numbers \( x \) such that \( x\geq0 \); among the given options, this is the most plausible as the other options (\( x\geq3 \) or \( x > 0 \)) don't fit if the graph starts at \( x = 0 \))