1. **Problem Statement:** Graph the polar curve given by the equation $$r = 4 + 4 \cos \theta$$. 2. **Identify the type of curve:** The general form of a limaçon is $$r = a + b \cos \theta$$ or $$r = a + b \sin \theta$$. 3. **Analyze parameters:** Here, $$a = 4$$ and $$b = 4$$. 4. **Determine the shape:** Since $$a = b$$, the curve is a cardioid, which is a special case of a limaçon that touches the pole (origin). 5. **Plot key points:** - At $$\theta = 0$$, $$r = 4 + 4 \times 1 = 8$$. - At $$\theta = \pi$$, $$r = 4 + 4 \times (-1) = 0$$ (curve hits the pole). - At $$\theta = \frac{\pi}{2}$$, $$r = 4 + 4 \times 0 = 4$$. 6. **Summary:** The curve is a cardioid that starts at the pole when $$\theta = \pi$$ and reaches a maximum radius of 8 at $$\theta = 0$$. **Final answer:** The polar curve $$r = 4 + 4 \cos \theta$$ is a cardioid that hits the pole.