y= log_{3 (x+4)}

We know log of zero is undefined. In the given problem we have log 0 when

x+4 =0 ie x =-4. So, x = -4 is the vertical asymptote to the curve.

Next log 1 is always zero for all bases. So, x =-3 gives x +4 =0. So we have the point (-3, 0) on the graph. Moreover, since the base is 3, when x+4 = 3, x = -1 the y is 1. Now with the three information

1. x =-4 is the asymptote,

2.(-3, 0) and

3. (-1,1) are points on the curve.

wecan now draw the graph.