f(x)=4x-3 is a linear function, the graph is a straight line.
when x=-1, f(x)=4(-1)-3=-7
when x=3, f(x)=4(3)-3=9
locate the two points (-1,-7) and (3,9). Notice the =sign in -1≤x≤3, so these two points are solid, not a bubble.
Connect the two points. the line segment is the graph.
so the overall graph will be a horizontal line 3 units below the x axis, coming from the left but stopping at (-1,-3), with the point (-1,-3) hollow; then a up-going line starting from (-1,-7) to (3,9), with both ends solid. and another up-going line starting from the hollow point (3,3), going through (4,4), (5,5)...
Does this make sense to you?