Question

Albert receives $0.30 per pound for 1 to 49 pounds of glass bottles he recycles. He receives $0.40

per pound if he recycles more than 50 pounds. Is the amount of money Albert receives a function
of the weight of the bottles he recycles? Explain your reasoning.

Answer 1

Yes

Explanation:

The amount of money Albert receives is described by the expression

`y = \begin{cases}0.30x  & \quad \text{if } 0 \leq x \leq 49 \\0.40x & \quad \text{if } x > 50\\\end{cases}`

The graph is shown below.

To determine if the relation is a function, we can use the vertical line test:

If a vertical line crosses the graph more than once in any location, the relation is not a function.

We see that at no place will a vertical line intersect the graph more than once.

The relation is a function.