Answer:
see attached
Explanation:
You want to graph the piecewise defined function ...
f(x) = 2x+9 for x < -3; 2x-2 for x > 4
Graph
You normally graph a line by finding (at least) two points on the line and drawing a line through them to make the graph. Often, it is convenient to start with the y-intercept. Here, it is convenient to start with the end point of the domain on which the line is defined. Additional points can be found by making use of the slope: rise 2 for each run of 1 to the right.
For x < -3, the value of y at x=-3 is ...
y = 2(-3) +9 = 3
So, the point (-3, 3) will appear on the graph. This point is not actually in the domain, which is x < -3, so will be graphed as an open circle. The line goes down and to the left from there with a slope of 2.
For x > 4, the value of y at x=4 is ...
y = 2(4) -2 = 6
So, the point (4, 6) will appear on the graph as an open circle, because x=4 is not actually in the domain of the function. The line will go up to the right from there with a slope of 2.
See the attachment for a finished graph.