1. **Stating the problem:** We are given a graph representing the detection function $f(x)$ of a Tesla Optimus robot's LIDAR sensor. The graph oscillates with diminishing amplitude centered at $x=0$, peaking sharply at $y=1$. 2. **Finding the function $f(x)$:** The description matches a damped oscillation, commonly modeled by the sinc function or a damped sine wave. A typical function is: $$f(x) = \frac{\sin(x)}{x}$$ which oscillates with decreasing amplitude as $|x|$ increases and peaks at $f(0)=1$ by limit. 3. **Explanation of the formula:** - The function $\frac{\sin(x)}{x}$ is defined as $1$ at $x=0$ by limit. - It oscillates between positive and negative values with amplitude decreasing as $x$ moves away from zero. 4. **Evaluating the limit as $x \to \infty$:** $$\lim_{x \to \infty} \frac{\sin(x)}{x} = 0$$ because $\sin(x)$ oscillates between $-1$ and $1$, but denominator $x$ grows without bound. 5. **Minimum values of $x$ and $y$ at limit $\infty$:** - As $x \to \infty$, $y = f(x) \to 0$. - The minimum value of $y$ in the limit is $0$. - $x$ tends to infinity. **Final answers:** - a) $f(x) = \frac{\sin(x)}{x}$ - b) At $x \to \infty$, $y_{min} = 0$ and $x$ tends to infinity.