Which graph represents y as a function of x?

The third picture (shown below as an attachment)

Step-by-step explanation:

This problem wants us to detect which one is a function. The definition of a function is that for every x-value you input into the function, you will get ONLY ONE y-value output. A way to check this when it’s graphed is to scan left to right (vice versa) and if there are two lines that meet at the same x-values, then it’s not a function. We can eliminate the circle graph because there are two lines that meet the x-coordinates. Like how when x is -5, the y-coordinate is both 7 and -7. This proves that for the x-coordinate -5, the y-coordinate has two y-coordinates, 7 and -7. Therefore, the circle graph is not a function. Same thing for the absolute value graph (the v-shape graph). There are two lines that overlap on the x-values. The last graph (the straight vertical line) is definitely not a function because all y-values are equal to the x-value 3, which means that multiple y-values share an x-coordinate. The third option (the correct one) is a function because there are no overlapping lines. You might say that when x is 1, there are two y-coordinates, 4 and -4. But the higher line has an open circle at 4 which means that the line doesn’t include 4. So they don’t overlap, which makes it a function. Choose the graph of option three (the attached picture).

I hope you understand.

Hope this helps and answers your question :)

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