1. The problem asks to find the values of $g(0)$, $g(0.0001)$, and $g(2.999)$ from the given piecewise graph of $y = g(x)$. 2. From the graph description: - There is a horizontal line segment from $x = -9$ to approximately $x = -4$ at $y = -5$. - There is a horizontal line segment from $x = 3$ to $x = 9$ at $y = 3$ with an open circle at $(3,3)$ and a closed circle at $(9,3)$. - There is a third isolated point or segment near $x = 0$ to $1$, $y = 3$. 3. Evaluate $g(0)$: - Since there is an isolated point or segment near $x=0$ to $1$ at $y=3$, and $0$ is within this range, $g(0) = 3$. 4. Evaluate $g(0.0001)$: - $0.0001$ is very close to $0$, so it lies in the same isolated segment near $x=0$ to $1$ at $y=3$, so $g(0.0001) = 3$. 5. Evaluate $g(2.999)$: - $2.999$ is just less than $3$, and the horizontal segment at $y=3$ starts at $x=3$ with an open circle (meaning $g(3)$ is not $3$), so for $x$ just less than $3$, the graph is not defined at $y=3$. - The graph description does not mention any segment between $-4$ and $3$, so $g(2.999)$ is undefined. 6. Summary: - $g(0) = 3$ - $g(0.0001) = 3$ - $g(2.999) = \text{Undefined}$