Is This Graph a Function? Apply the Vertical Line Test

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
00:00 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 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 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.

3

Final Answer

Yes

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

XY02468-3-3-3-3-3

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