Piecewise Function 8540D4

1. **State the problem:** We need to graph the piecewise function $$g(x) = \begin{cases} 1 & \text{if } x < 0 \\ -2 & \text{if } x = 0 \\ -1 & \text{if } x > 0 \end{cases}$$ 2. **Understand the function:** The function $g$ takes different constant values depending on whether $x$ is less than, equal to, or greater than zero. 3. **Graph for $x < 0$:** The function value is $1$. This means for all $x$ less than zero, $g(x) = 1$. We draw a horizontal line at $y=1$ for $x<0$. 4. **Open circle at $(0,1)$:** Since the function is not defined as $1$ at $x=0$, we place an open circle at $(0,1)$ to indicate the value is not included there. 5. **Value at $x=0$:** The function value is $-2$. We plot a filled point at $(0,-2)$ to show the function value at zero. 6. **Graph for $x > 0$:** The function value is $-1$. For all $x$ greater than zero, $g(x) = -1$. We draw a horizontal line at $y=-1$ for $x>0$. 7. **Open circle at $(0,-1)$:** Since the function is not defined as $-1$ at $x=0$, we place an open circle at $(0,-1)$. **Final graph description:** - Horizontal line at $y=1$ for $x<0$ with an open circle at $(0,1)$. - Filled point at $(0,-2)$. - Horizontal line at $y=-1$ for $x>0$ with an open circle at $(0,-1)$. This completes the graph of the piecewise function $g$.