Answer:

Explanation:
The given graph is the graph of a piecewise function.
A piecewise function is a combination of various graphs, each reflecting the behavior of the function on a distinct interval.
The given graph has two straight lines:
- Line 1 (positive slope) has a closed circle at the endpoint (-2, -3), and continues indefinitely in the upper-right direction after passing through point (3, 2).
- Line 2 (negative slope) has an open circle at the endpoint (-2, 2), and continues indefinitely in the upper-left direction after passing through point (-5, 5).
To write the piecewise function, we need to find the equations of the two lines by finding their slopes, then substituting the slopes and one of the points into the point-slope form of a linear equation.


Line 1
To find the slope (m) of line 1, substitute the endpoint (-2, -3) and the point on the line (3, 2) into the slope formula:

Now, substitute the found slope and one of the points into the slope-point formula:

Therefore, the equation of line 1 is:

As there is a closed circle at endpoint (-2, -3), the value of x = -2 is included in the interval for this piece of the function. Therefore, the interval for y = x - 1 is x ≥ -2.
Line 2
To find the slope (m) of line 2, substitute the endpoint (-2, 2) and the point on the line (-5, 5) into the slope formula:

Now, substitute the found slope and one of the points into the slope-point formula:

Therefore, the equation of line 2 is:

As there is an open circle at endpoint (-2, 2), the value of x = -2 is not included in the interval for this piece of the function. Therefore, the interval for y = -x is x < -2.
Solution
Therefore, the piecewise function for the given graph is:
