Vertical Line Test: Is This Curved Graph a Function?

Function Definition with Graphical Analysis

Determine whether the given graph is 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 each X value has one Y value
00:09 Let's check the graph values in the table
00:18 We can see that each value has only one Y value, therefore it's a function
00:24 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

Determine whether the given graph is 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

It is important to remember that a function is an equation that assigns to each element in domain X one and only one element in range Y

We should note that for every X value found on the graph, there is one and only one corresponding Y value.

Therefore, the graph is indeed a function.

3

Final Answer

Yes

Key Points to Remember

Essential concepts to master this topic
  • Function Rule: Each x-value must have exactly one y-value
  • Vertical Line Test: Draw vertical lines - if any crosses graph twice, not a function
  • Check: Every vertical line through this curve hits only one point ✓

Common Mistakes

Avoid these frequent errors
  • Confusing functions with relations
    Don't think every graph is automatically a function = wrong classification! A relation becomes a function only when each input has exactly one output. Always apply the vertical line test to check if any x-value produces multiple y-values.

Practice Quiz

Test your knowledge with interactive questions

Determine whether the following table represents a constant function:

XY02468-3-3-3-3-3

FAQ

Everything you need to know about this question

What exactly is the vertical line test?

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The vertical line test is a visual way to check if a graph represents a function. Draw imaginary vertical lines through the graph - if any vertical line crosses the curve more than once, it's not a function.

Why does this curved graph pass the test?

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Looking at this curve, every vertical line you could draw would intersect it at exactly one point. This means each x-value corresponds to only one y-value, satisfying the function definition.

What would make a graph fail the vertical line test?

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Graphs like circles, sideways parabolas, or any curve where you can draw a vertical line that hits two or more points would fail the test and not be functions.

Is every function a relation?

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Yes! Every function is a relation, but not every relation is a function. A function is a special type of relation where each input has exactly one output.

Can a function have the same y-value for different x-values?

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Absolutely! Multiple x-values can share the same y-value. The restriction is only that each x-value must map to exactly one y-value, not the other way around.

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