1. The problem is to evaluate the step function $g(x)$ at specific points: $g(0)$, $g(0.0001)$, $g(2.999)$, and $g(3)$, and analyze the behavior of the function. 2. Step functions are constant on intervals and may have jumps at certain points. The value of $g(x)$ is constant within each interval but can change abruptly at the boundaries. 3. Given the graph description, $g(x)$ is constant at $y=3$ for the interval around $x=0$. This means for $x$ in $[-9,0)$, $g(x)=3$. 4. Evaluate $g(0)$: Since the function is a step function, the value at the boundary depends on the graph. Usually, the value at $x=0$ is the value of the step at that point. From the description, $g(0)=3$. 5. Evaluate $g(0.0001)$: This is just to the right of 0. If the step changes at 0, $g(0.0001)$ might be different. But from the description, the step at $x=0$ is $3$, so $g(0.0001)=3$. 6. Evaluate $g(2.999)$: This is just before $x=3$. The function value here depends on the step at the interval before 3. From the graph, the value is $3$. 7. Evaluate $g(3)$: At $x=3$, the function is undefined or has a jump. The problem states "Undefined" at 3, so $g(3)$ is undefined. 8. Summary: - $g(0)=3$ - $g(0.0001)=3$ - $g(2.999)=3$ - $g(3)$ is undefined This matches the behavior of a step function with a jump discontinuity at $x=3$.