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Does this graph show a function? Explain how you know.
A. No; there are y-values that have more than one x-value.
B. No; the graph fails the vertical line test.
C. Yes; the graph passes the vertical line test.
D. Yes; there are no y-values that have more than one x-value.
To check a graph whether it’s a function or not we use a vertical line test. In this test first we draw a vertical line on the given graph. If this line intersects the graph at more than one point, the graph is not a function.
In the given parabola, opening upwards passes the vertical line test.
Therefore, this graph shows a function.
Option (C) will be the answer.
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