1. **Stating the problem:** We have a function machine that takes inputs $15y$, $15w$, and $15p$ and outputs $y$, $w$, and $p$ respectively. 2. **Understanding the function:** The machine transforms each input by dividing by 15 to get the output. For example, input $15y$ becomes output $y$. 3. **Formula used:** To find the output from the input, use the formula $$\text{output} = \frac{\text{input}}{15}$$ 4. **Applying the formula:** - For input $15y$, output is $$\frac{15y}{15} = \cancel{15}y/\cancel{15} = y$$ - For input $15w$, output is $$\frac{15w}{15} = \cancel{15}w/\cancel{15} = w$$ - For input $15p$, output is $$\frac{15p}{15} = \cancel{15}p/\cancel{15} = p$$ 5. **Conclusion:** The function machine divides each input by 15 to produce the output. **Final function:** $$f(x) = \frac{x}{15}$$ where $x$ is any of the inputs $15y$, $15w$, or $15p$.