Question

Do the following points represent a function? (0,2) (1,4) (0,4) (3,9) (5,8)​

Answer 1

Answer: No, this isn't a function.

Why not? Focus on the two points (0,2) and (0,4)

We have the x value x = 0 show up twice. Any time x repeats itself like this, it leads to "not a function" as the result.

In other words, the input x = 0 leads to multiple outputs y = 2 and y = 4 at the same time. A function is only possible if every x input leads to exactly one y output.

If you are a visual learner, then plot all of the points on the same xy grid. Then notice how (0,2) and (0,4) fail the vertical line test to show we don't have a function.

Side note: The y values can repeat themselves in a function.