At the overlap (the y-axis, where x=0), put a filled-in dot wherever sqrt(x) + 4 hits the y-axis. This shows that your final function *includes* this point, since you’re graphing sqrt(x) + 4 for all x greater than OR EQUAL TO zero. Put a hollow circle wherever -x-1 hits the y-axis. This shows that your final graph does *not* include this point, since you are graphing -x-1 for all x less than BUT NOT EQUAL TO zero.

Remember that for your function to be a function it has to have at most one y-value for each x-value. In other words, it should pass the vertical line test. A vertical line drawn anywhere in the graph can intersect the graph only once. The filled in circle for sqrt(x) + 4 and the hollow circle for -x-1 at the y-axis show that a vertical line drawn through the y-axis would still hit your graph only once.