Question: top-left: Graph $y = f(x)$ by hand by first plotting points to determine the shape of the graph. top-left: $f(x) = 0$ top-left: Use the graphing tool to graph the equation. top-left: Click to enlarge graph top-right: Coordinate grid with x-axis and y-axis labeled from -10 to 10; the graphing area is empty and shows only the axes and grid lines.

1. The problem asks us to graph the function $f(x) = 0$ by plotting points to determine the shape of the graph. 2. The function $f(x) = 0$ means that for every value of $x$, the output $y$ is always $0$. 3. To plot points, choose several values of $x$ and calculate $f(x)$: - For $x = -2$, $f(-2) = 0$ - For $x = 0$, $f(0) = 0$ - For $x = 3$, $f(3) = 0$ 4. All points lie on the line where $y = 0$, which is the x-axis. 5. Therefore, the graph of $f(x) = 0$ is a horizontal line along the x-axis. 6. Using the graphing tool, plot the points $(-2,0)$, $(0,0)$, and $(3,0)$ and draw a straight horizontal line through them. 7. This confirms the shape of the graph is a horizontal line at $y=0$ across all $x$ values.