1. **Problem Statement:** We are given a cosine graph that is horizontally shifted. We need to find the equations for the closest left and right horizontal shifts of the form $$y = \cos(x - c)$$ where $c$ is the shift. 2. **Recall the standard cosine function:** The standard cosine function is $$y = \cos x$$ which has peaks at multiples of $2\pi$, i.e., at $x = 0, \pm 2\pi, \pm 4\pi, \ldots$. 3. **Horizontal shift rule:** A function $$y = \cos(x - c)$$ is shifted to the right by $c$ units if $c > 0$, and to the left by $|c|$ units if $c < 0$. 4. **Identify the shift from the graph:** The graph shows a right shift relative to the standard cosine wave. The closest right shift corresponds to the smallest positive $c$ such that the wave aligns with the standard cosine wave pattern. 5. **Determine the shift value $c$:** Since the wave is shifted right, the closest right shift $c$ is the horizontal distance from $0$ to the first peak on the right side. This is typically between $0$ and $2\pi$. 6. **Calculate the closest left shift:** The closest left shift corresponds to a negative $c$ value that shifts the wave left to align with the standard cosine wave. This is the negative of the closest right shift. 7. **Express the equations:** - Closest left shift: $$y = \cos\left(x - (-c)\right) = \cos(x + c)$$ - Closest right shift: $$y = \cos(x - c)$$ 8. **Rounding:** Round $c$ to two decimal places. **Final answers:** - Closest left shift: $$y = \cos(x - (-c)) = \cos(x + c)$$ - Closest right shift: $$y = \cos(x - c)$$ Since the exact shift $c$ is not numerically given in the problem, it must be measured from the graph. Assuming the shift is approximately $\frac{\pi}{4} \approx 0.79$, the answers are: - Closest left shift: $$y = \cos(x + 0.79)$$ - Closest right shift: $$y = \cos(x - 0.79)$$