Question

Which relation is a function?

Answer 1

The last graph (absolute value graph with a “v” shaped line) represents a function.

By definition, A function is a relation in which no two ordered pairs have the same input (or x-values) and different outputs (y-values).

A great way to determine whether a graph represents a function is by doing a Vertical Line Test.

The Vertical Line Test allows us to know whether or not a graph is actually a function. If a vertical line intersects the graph in all places at exactly one point, then the relation is a function.

To use the vertical-line test, imagine dragging a ruler held vertically across the
graph from left to right. If the graph is that of a function, the edge of the ruler would hit the graph only once for every x -value.

Attached is an edited version of the image you’ve uploaded where I did the Vertical Line Test (sorry for poor editing, I’m using my phone at the moment while typing this answer). The first graph with a circle shows that each vertical line contains more than 1 red point in it. It means that it the x-values have more than 1 corresponding y-value.

The 2nd graph (horizontal parabola) also failed the VLT because each vertical line drawn contained more than 1 point in it, meaning each vertical line drawn crossed the graph more than once.

The 3rd graph is a vertical line, which obviously failed the VLT because it contained more than 1 point.

The last graph (absolute value graph) passed the VLT because each vertical line contains only 1 point at most. Therefore, it is the correct answer.

Please mark my answers as the Brainliest if you find this helpful :)

Answer 2

It's the one second below the question because it does not have two outcomes for x. For example in a relation x could result in y = 2 or y = -2.

Hope this helps! :)