Question

six graphs are shown below. click on the tabs to see them. check the box corresponding to each graph that represents a function. graph 1 graph 2 graph 3 graph 4 graph 5 graph 6 none of the graphs

Explanation:

Step1: Recall vertical - line test

A graph represents a function if for every x - value in the domain, there is exactly one y - value. Mathematically, no vertical line should intersect the graph at more than one point.

Step2: Apply to Graph 2

Examine Graph 2. For all x - values in its domain, a vertical line will intersect the graph at most once.

Answer:

To determine if a graph represents a function, we use the vertical - line test. If any vertical line intersects the graph at more than one point, then the graph does not represent a function. Since we only have Graph 2 shown here, we need to apply the vertical - line test to it.
For Graph 2:

• Consider the left - most part of the graph which is a line segment from a closed - point to an open - point. Then there is another line segment starting from a closed - point. And then a horizontal line segment.
• If we draw a vertical line through the x - values where the graph has breaks or jumps, we see that for each x - value in the domain of the graph, there is exactly one y - value. So Graph 2 represents a function.

So the answer is Graph 2.