A relation is a function if each input gives exactly one output. There is one price for each number of pounds, so the relation is a function.
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<em>Additional comment</em>
Relations expressed in terms of ordered pairs or tables can be identified as "not a function" if any input (x) value is repeated. Relations expressed as a graph will be "not a function" if any vertical line intersects the graph at more than one point. (This is called "the vertical line test.")
The cost function in this case is a straight line through the origin. It has a slope of $5.99/lb. Any polynomial relation will be a function.
