Question

use the vertical line test to determine if y is a function of x in the graph.
which of the following statements is correct? choose the correct answer below.
y is a function of x
y is not a function of x

Explanation:

Step1: Recall Vertical Line Test

The vertical line test states that a graph represents \( y \) as a function of \( x \) if no vertical line intersects the graph at more than one point.

Step2: Analyze the Graph

The given graph appears to be a horizontal line (or two horizontal lines? Wait, looking at the graph, it's a horizontal line? Wait, the graph shown has a horizontal line (or maybe two parallel horizontal lines? Wait, no, maybe it's a horizontal line. Wait, no, the user's graph: let's see, the graph has a horizontal line (or maybe two? Wait, no, the key is vertical line test. For a horizontal line (like \( y = k \) for some constant \( k \)), any vertical line \( x = a \) will intersect the horizontal line at exactly one point (\( (a, k) \)). Wait, but if there are two horizontal lines (like two parallel lines), then a vertical line would intersect both, meaning two points, so not a function. Wait, the graph in the problem: let's re-examine. The user's graph: there are two horizontal lines? Wait, the image shows two horizontal lines? Wait, no, maybe it's a typo, but the options: if the graph is such that a vertical line intersects it at more than one point, then it's not a function. Wait, wait, the original problem: the graph has two horizontal lines? Wait, no, maybe the graph is two horizontal lines (like \( y = c_1 \) and \( y = c_2 \), \( c_1
eq c_2 \)). Then a vertical line \( x = a \) would intersect both lines, so two points, so \( y \) is not a function of \( x \). Wait, but let's check the options. The options are "y is a function of x" or "y is not a function of x". Wait, maybe the graph has two horizontal lines, so a vertical line intersects at two points. So the correct answer is "y is not a function of x". Wait, but let's confirm. The vertical line test: if any vertical line intersects the graph at more than one point, then \( y \) is not a function of \( x \). If the graph has two horizontal lines, then a vertical line will cross both, so two points. Hence, \( y \) is not a function of \( x \).

Answer:

y is not a function of x