Graph the relation shown in the table. is the relation a function? why or why not? {(–3, –2), (–1, 0), (1, 0), (5, –2)} no; the relation passes the vertical-line test. yes; only one range value exists for each domain value. yes; two domain values exist for range value –2. no; two domain values exist for range value –2.

choice B) yes; only one range value exists for each domain value

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Explanation:

The inputs are x = -3, x = -1, x = 1, x = 5. They are the first coordinate listed of each point. We don't have any x values repeating so this means we have a function. Each input leads to exactly one output which is what choice B is stating. The domain is the set of allowed inputs, or x values. The range is the set of possible y outputs. 

If we had something like (1,2) and (1,5) then the input x = 1 leads to more than one output (y = 2 and y = 5). This example means we don't have a function

If you graph the points (-3, -2), (-1,0), (1,0) and (5,-2) as shown in the attached image, then you'll notice that it is impossible to pass a single line through more than one point. Therefore this graph passes the vertical line test visually proving we have a function. 

Going back to the example with (1,2) and (1,5), plotting these two points leads to the vertical line test failing implying we don't have a function.