1. **Evaluate the limit**: $$\lim_{x \to -4} (x + 3)$$ 2. **State the problem**: We want to find the value that the function $f(x) = x + 3$ approaches as $x$ gets closer to $-4$. 3. **Use the limit property for polynomials and linear functions**: The limit of a polynomial or linear function as $x$ approaches a value is simply the function evaluated at that value. 4. **Calculate the limit**: $$\lim_{x \to -4} (x + 3) = (-4) + 3 = -1$$ 5. **Construct the table of values**: | $x$ | -5 | -4.5 | -4.1 | -4 | -3.9 | -3.5 | -3 | |-----|----|------|------|----|------|------|----| | $f(x)$ | -2 | -1.5 | -1.1 | -1 | -0.9 | -0.5 | 0 | 6. **Interpretation**: As $x$ approaches $-4$ from both sides, $f(x)$ approaches $-1$. 7. **Graph sketch description**: The graph of $f(x) = x + 3$ is a straight line with slope 1 and y-intercept 3. Near $x = -4$, the function value is close to $-1$. **Final answer:** $$\boxed{-1}$$