Question

what is the domain of the function? \\( \bigcirc \\ x > -2 \\) \\( \bigcirc \\ x > 0 \\) \\( \bigcirc \\ x < 2 \\) \\( \bigcirc \\) all real numbers

Explanation:

Step1: Understand Domain Definition

Domain is the set of all possible \( x \)-values for a function. We analyze the graph's horizontal extent.

Step2: Analyze the Graph's Horizontal Range

The graph starts at \( x = -2 \) (the leftmost point, with a closed or open? Wait, the left end is a vertical asymptote? Wait, no, the graph has a point at \( x = -2 \)? Wait, looking at the graph: the leftmost part is at \( x = -2 \) (the curve starts there, with a closed dot? Wait, the graph shows the curve starting at \( x = -2 \) (the left end, the point where it starts, and then extends to the right infinitely. Wait, no, the left side: the graph has a vertical asymptote? Wait, no, the graph's leftmost \( x \)-value is \( x > -2 \)? Wait, no, looking at the graph, the left end is at \( x = -2 \) (the curve starts at \( x = -2 \), and then goes to the right. Wait, no, the graph's domain: the leftmost \( x \) is \( x = -2 \)? Wait, no, the graph shows that the function is defined for all \( x \) greater than \( -2 \)? Wait, no, wait the options: the first option is \( x > -2 \). Wait, let's check the graph again. The graph starts at \( x = -2 \) (the leftmost point, where the curve begins, and then extends to the right. Wait, no, the left side: the graph has a vertical asymptote? No, the graph's left end is at \( x = -2 \), and then it goes to the right. Wait, but the options: the first option is \( x > -2 \). Wait, maybe the graph's domain is all \( x \) such that \( x > -2 \). Wait, let's re-examine: the graph starts at \( x = -2 \) (the leftmost \( x \)-value, and then continues to the right. So the domain is \( x > -2 \)? Wait, no, wait the options: the first option is \( x > -2 \), second \( x > 0 \), third \( x < 2 \), fourth all real numbers. Wait, maybe I made a mistake. Wait, the graph: the left end is at \( x = -2 \), and the graph extends to the right. So the domain is \( x \geq -2 \)? But the first option is \( x > -2 \). Wait, maybe the graph has a vertical asymptote at \( x = -2 \), so \( x > -2 \). So the correct option is \( x > -2 \).

Answer:

A. \( x > -2 \)