Determine Function: Vertical Line Validation on Given Graph

Question

Is the given graph a function?

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Video Solution

Solution Steps

00:00 Is the graph a function?
00:05 The definition of a function is that for each Y value there is one X value
00:10 It seems there are multiple values for the same X value in the graph
00:15 Therefore the graph is not a function Y is not
00:18 A line parallel to the Y-axis is never a function
00:21 And this is the solution to the question

Step-by-Step Solution

To determine whether the graph represents a function, we apply the Vertical Line Test. Here are the steps we follow:

  • Step 1: Visualize placing a vertical line across various parts of the graph.
  • Step 2: Check if the vertical line intersects the graph at more than one point at any given position.

Step 1: On evaluating the given graph carefully, there is a notable presence of a vertical line passing through multiple y-values. Specifically, the vertical line goes from y=−3 y = -3 to y=3 y = 3 at x=3 x = 3 .

Step 2: Since this vertical line at x=3 x = 3 intersects the graph at an infinite number of points, it fails the Vertical Line Test.

Therefore, the graph does not represent a function. According to our analysis and the Vertical Line Test, the correct answer is No.

Answer

No

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