1. **Problem Statement:** We are given two functions, a rational function $f(x)$ and an absolute value function $g(x)$, graphed on the coordinate plane. We need to find the intervals among the given options where the equation $f(x) = g(x)$ has solutions. 2. **Understanding the Functions:** - The absolute value function $g(x)$ has a V-shape with vertex near $(-1, -3)$. - The rational function $f(x)$ has a vertical asymptote at $x=0$ and approaches the x-axis as a horizontal asymptote. 3. **Key Idea:** Solutions to $f(x) = g(x)$ occur where the graphs intersect. 4. **Analyzing Intervals:** - For $x < 0$, the rational function $f(x)$ is negative and tends to $-\\infty$ near $x=0$ from the left. - The absolute value function $g(x)$ is always non-negative or negative near its vertex at $(-1, -3)$. 5. **Checking intervals:** - **A. $-4 < x < -3$:** No intersection visible; $g(x)$ is high, $f(x)$ is low. - **B. $-3 < x < -2$:** No intersection visible. - **C. $-2 < x < -1$:** The graphs appear to cross near the vertex of $g(x)$. - **D. $-1 < x < 0$:** No intersection; $f(x)$ drops sharply, $g(x)$ rises. - **E. $0 < x < 1$:** No intersection; $f(x)$ is positive and decreasing, $g(x)$ is positive and increasing. - **F. $1 < x < 2$:** No intersection visible. - **G. $2 < x < 3$:** Intersection visible near $(3,1)$. - **H. $3 < x < 4$:** No intersection visible. 6. **Conclusion:** The intervals containing solutions to $f(x) = g(x)$ are **C** and **G**. **Final answer:** Intervals $-2 < x < -1$ and $2 < x < 3$ contain solutions.