Question

Does this graph represent a function? Why or why not?

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A. No, because it fails the vertical line test.
B. No, because it is not a straight line.
O C. Yes, because it is a curved line.
D. Yes, because it passes the vertical line test.
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Answer 1

Answer: D. Yes. It passes the vertical line test

Ask yourself if it is possible to draw a single straight line through more than one point on the red curve. If it is possible, then the graph is said to fail the vertical line test. Otherwise, the graph passes the test.

In terms of algebra, any input x value leads to one and only one y output value. This is what defines a function. If you had x lead to more than one output, then we wouldn't have a function. Of course, the x value must be in the domain.