1. **State the problem:** We need to estimate the value of $k(j(2))$ using the given graphs of $j(x)$ and $k(x)$ for $-1 \leq x \leq 5$. 2. **Find $j(2)$ from the graph of $j(x)$:** - The graph of $j(x)$ is piecewise linear, rising from $(-1,-1)$ to $(3,5)$. - At $x=2$, which lies between $-1$ and $3$, the value of $j(2)$ is approximately on the line between $(-1,-1)$ and $(3,5)$. - The slope of this segment is $\frac{5 - (-1)}{3 - (-1)} = \frac{6}{4} = 1.5$. - Using point-slope form from $(-1,-1)$: $$j(2) = -1 + 1.5 \times (2 - (-1)) = -1 + 1.5 \times 3 = -1 + 4.5 = 3.5$$ 3. **Find $k(j(2)) = k(3.5)$ from the graph of $k(x)$:** - The graph of $k(x)$ is an increasing curve approaching 6 as $x$ approaches 5. - At $x=3.5$, the value of $k(x)$ is approximately between 5 and 6, closer to 5.5. 4. **Conclusion:** $$k(j(2)) \approx k(3.5) \approx 5.5$$ Thus, the estimated value of $k(j(2))$ is approximately **5.5**.