Question

use the graph to answer problems 4 - 5.

1. construct arguments does the graph represent a function? explain.
2. name a section of the graph that, taken in isolation, is a function.

Explanation:

Step1: Check the vertical line test

A function is a relation where each input (x - value) has exactly one output (y - value). The vertical line test states that if a vertical line intersects the graph at more than one point, the graph does not represent a function.
Looking at the given graph, we can see that there are vertical lines (for example, a vertical line around \(x = 6\)) that intersect the graph at more than one point.

Step2: Analyze a section for a function

For a section to be a function, it must pass the vertical line test. Consider the right - most part of the graph (for example, the part of the graph where \(x\geq8\)). A vertical line drawn on this part of the graph will intersect the graph at only one point.

Answer:

1. The graph does not represent a function. Because by the vertical - line test, there are vertical lines that intersect the graph at more than one point.
2. The right - most part of the graph (where \(x\geq8\)) is a section of the graph that, taken in isolation, is a function.