Determine Function: Vertical Line Validation on Given Graph

Is the given graph a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:02 Let's find out if the graph is a function.
00:07 A function means each x-value has exactly one y-value.
00:12 Here, it looks like one x-value has multiple y-values.
00:17 So, this graph is not a function.
00:21 Remember, a line parallel to the y-axis is not a function.
00:25 And that's how we solve this question.

Step-by-step written solution

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1

Understand the problem

Is the given graph a function?

–7–7–7–6–6–6–5–5–5–4–4–4–3–3–3–2–2–2–1–1–1111222333444555666777–4–4–4–3–3–3–2–2–2–1–1–1111222333000

2

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.

3

Final Answer

No

Practice Quiz

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Determine whether the following table represents a constant function:

XY02468-3-3-3-3-3

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