To determine whether the given piecewise function \( f(x) \) matches the description of the graph with open and closed endpoints, we will analyze the conditions of the function.
The piecewise function is defined as follows:
- \( f(x) = x + 2 \) if \( x < -2 \)
- \( f(x) = 5 + x \) if \( -2 \leq x < 4 \)
- \( f(x) = -2x + 7 \) if \( x \geq 4 \)
Now, let’s check for the endpoints:
- The first piece (\( x + 2 \)) applies to values less than -2, so it does not include -2 (open endpoint).
- The second piece includes -2 (closed endpoint) and goes up to but does not include 4 (open endpoint).
- The third piece includes 4 (closed endpoint) and applies for values greater than or equal to 4.
Next, we interpret what these conditions would look like graphically:
- The line \( x + 2 \) falling to the left of -2 would be an open point at (-2, 0).
- The line \( 5 + x \) would have a closed point at (-2, 3) and an open point at (4, 9).
- The line \( -2x + 7 \) would begin at (4, -1) and continue to the right, including the point (4, -1).
Without the actual image, we can't definitively know how these pieces are represented visually. However, given the description of one closed endpoint and two open endpoints, it seems plausible that the function as proposed is accurately represented by those graphical conditions.
So if the interpretation of the lines matches the piecewise function's definitions, the answer would be:
1 for true.
If there is any divergence in the graphical representation (considering aspects like slopes or exact intersections), the answer would be 2 for false.
Since I cannot see the image, I can only guide you to assess if those endpoints match the behavior I've described from the function's definition.