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Which graph represents y as a function of x?

Which graph represents y as a function of x?-example-1
User Robottinosino
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1 Answer

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14 votes

Answer: Graph C

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Reason:

This graph passes the vertical line test, so it is a function.

The vertical line test is where we try to pass a single vertical line through more than one point on the curve. If such a thing is possible, then we say the curve fails the vertical line test and it's not a function.

Graph D for instance can have a vertical line through x = 1 and intersect the curve at (1,4) and (1,-4) simultaneously. The input x = 1 leads to multiple outputs (y = 4 and y = -4). Graph D fails the vertical line test for this very reason, and it is not a function. Graphs A and B are similar stories. Any vertical line itself is automatically not a function.

To have a function, any x input in the domain must lead to exactly one and only one y output in the range.

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Notice with graph C it is impossible to have a single vertical line intersect more than one point on the curve. So this is why graph C passes the vertical line test. Each input leads to exactly one output.

User Jakobandersen
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