the piece - wise function h(x) is shown on the graph. what is the value of x when h(x)=-3? -7 -1 0 2

Explanation:

Step1: Identify the value on the y-axis.

Locate the value $h(x) = -3$ on the vertical axis (y-axis) of the provided graph.

Step2: Find the corresponding x-value(s) on the graph.

Draw a horizontal line from $y = -3$ to intersect the graph of the piecewise function $h(x)$. Observe the x-coordinate(s) of the intersection point(s). The line $y=-3$ intersects the graph on the left line segment. Visually, this intersection occurs between $x=-1$ and $x=0$. The line $y=-3$ also aligns with the open circle endpoint of the right line segment at $x=3$.

Step3: Determine the valid x-value from the intersection.

The intersection point on the left segment corresponds to a valid x-value because the segment is solid. The point at $x=3$ is an open circle, meaning $h(3) \neq -3$, so $x=3$ is not a solution. The intersection on the left segment appears to be at $x = -0.5$.

Step4: Check the options.

The calculated value $x = -0.5$ is not listed in the options: -7, -1, 0, 2. This indicates a potential issue with the graph or the options provided. However, if we assume a possible error in the graph's drawing, specifically if the first segment was intended to pass through $(-1, -3)$, then $x=-1$ would be the solution. Let's verify the coordinates used to define the first segment: $(-2, -7)$ and $(1, 1)$. The slope is $m = \frac{1 - (-7)}{1 - (-2)} = \frac{8}{3}$. The equation is $y - 1 = \frac{8}{3}(x - 1)$, or $y = \frac{8}{3}x - \frac{5}{3}$. Setting $y = -3$, we get $-3 = \frac{8}{3}x - \frac{5}{3}$, which leads to $8x = -4$, so $x = -1/2$. Since $-1/2$ is not an option, and assuming there might be an intended integer answer possibly due to graph inaccuracy or typo (e.g., vertex intended at (0,1) instead of (1,1), which would yield $x=-1$), we select the closest plausible option. Option B is $x=-1$.

Answer:

B. -1