Question

Which of the following is an example of a function?

{(-1, 0), (-1, 3), (3, 9), (5, 10}


{(1, 3), (2, 5), (3, 8), (4, 10)}


{(4, 6), (5, 9), (4, 7)}


{(0, 2), (0, 3), (1, 5), (4, 5)}

Answer 1

A. Not a function since we have the points (-1,0) and (-1,3). The x value repeats while the y values are different. Plugging in x = -1 leads to multiple outputs, which shows we don't have a function. To get a better visual, you can plot the points. You'll see that the points form a vertical line. Therefore, this graph fails the vertical line test.

B. This is a function. All of the x values are different. The points, when graphed, pass the vertical line test. In other words, its impossible to draw a vertical line through any two points on the graph. Any x input here leads to exactly one y output.

C. This is not a function. Like choice A, we have repeated x values. In this case we have (4,6) and (4,7). The x value x = 4 repeats itself leading to multiple outputs y = 6 and y = 7

D. This is also not a function. The x value x = 0 repeats itself. The graph fails the vertical line test.

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Answer: Choice B