Question: User: 1)\nx 1 2 3 4\ny 100 50 33 25\ntable graph in top-left, showing x-values 1, 2, 3, 4 across the top row and y-values 100, 50, 33, 25 across the bottom row.
1. **Problem Statement:** We are given a table of values for $x$ and $y$:\\
\begin{array}{c|cccc}
x & 1 & 2 & 3 & 4 \\
y & 100 & 50 & 33 & 25 \\\end{array}\\
We want to analyze the relationship between $x$ and $y$.\\
\\
2. **Observing the pattern:** Notice how $y$ changes as $x$ increases.\\
- When $x=1$, $y=100$.\\
- When $x=2$, $y=50$.\\
- When $x=3$, $y=33$.\\
- When $x=4$, $y=25$.\\
\\
3. **Hypothesis:** The values suggest an inverse relationship between $x$ and $y$. Let's check if $y$ is proportional to $\frac{1}{x}$.\\
\\
4. **Testing the inverse proportionality:** Calculate $x \times y$ for each pair:\\
$$1 \times 100 = 100$$\\
$$2 \times 50 = 100$$\\
$$3 \times 33 = 99$$ (approximately 100)\\
$$4 \times 25 = 100$$\\
\\
5. Since $x \times y \approx 100$ for all pairs, we conclude that $y$ is inversely proportional to $x$ with constant $k = 100$.\\
\\
6. **Formula:** The relationship can be expressed as:$$y = \frac{100}{x}$$\\
\\
7. **Explanation:** This means as $x$ increases, $y$ decreases such that their product remains constant at 100.\\
\\
**Final answer:** The function relating $x$ and $y$ is $$\boxed{y = \frac{100}{x}}$$.