1. **State the problem:** We are given a function $f(x)$ with points $(1,5)$, $(0,1)$, and $(-1, \frac{1}{5})$. We need to analyze the graph of $g(x)$, describe the transformation from $f(x)$ to $g(x)$, and write $g(x)$ in terms of $f(x)$. 2. **Identify the transformation:** The points on $f(x)$ are $(1,5)$, $(0,1)$, and $(-1, \frac{1}{5})$. If $g(x)$ corresponds to these points but with $y$-values inverted, for example, $g(1) = \frac{1}{5}$, $g(0) = 1$, and $g(-1) = 5$, then $g(x)$ is the reciprocal of $f(x)$. 3. **Write the transformation formula:** The transformation is a reflection over the line $y=1$ in terms of reciprocal values, so $$g(x) = \frac{1}{f(x)}$$ 4. **Explain:** This means for each $x$, the value of $g(x)$ is the reciprocal of $f(x)$. For example, since $f(1) = 5$, then $g(1) = \frac{1}{5}$. 5. **Final answer:** $$g(x) = \frac{1}{f(x)}$$