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For a relation to be a function, each $x$-value can only be paired with one $y$-value, but one $y$-value can be paired with multiple $x$-values. In a graph, we can check if each $x$-value has only one $y$-value by subjecting it to the vertical line test.
On the given graph, there is no visible part where two points have the same $y$-value. Each vertical line passes through the graph at only one point, so the graph is a function.