Is This Graph a Function? Apply the Vertical Line Test

Question

Is the given graph a function?

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Video Solution

Solution Steps

00:00 Is the given graph a function?
00:05 The definition of a function is that for each X value there is one Y value
00:08 Let's check the graph values in the table to determine if it's a function
00:25 We can see that for each X value there is one Y value, therefore it's a function
00:29 And this is the solution to the question

Step-by-Step Solution

To determine if the graph in question represents a function, we'll employ the Vertical Line Test. This test helps to ascertain whether each input value from the domain (x-values) is connected to a unique output value (y-values).

  • According to the Vertical Line Test, a graph represents a function if no vertical line can intersect the graph at more than one point.
  • In the provided diagram, the graph is a straight line.
  • Visual inspection shows that any vertical line drawn at any point along the x-axis intersects the line exactly once.
  • This indicates that for each x-value, there is a unique corresponding y-value. Therefore, the relationship depicted by the graph meets the criteria for a function.

Thus, the given graph correctly characterizes a function.
Therefore, the solution to the problem is Yes.

Answer

Yes

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