The #x#-intercept of a logarithmic function #f(x)=log_a(x)# occurs wherever #x=1# (because #log_a(1)=0#); therefore, we want to solve whatever is in the argument (parentheses) of the logarithmic function for #1:#
#x+2=1#
#x=1-2=-1#
Thus, the #x#-intercept occurs at #(-1,0)#.
The vertical asymptote of a logarithmic function #f(x)=log_a(x)# occurs at #x=c# where #c# is the number at which the argument (parentheses) of the logarithmic function becomes #0#, because we know #f(x)=log_a(x)# does not exist for #x<0#. This means we need to solve whatever is in the parentheses of our logarithmic function for #0.#
#x+2=0#
#x=-2#
Thus, #x=-2# is the vertical asymptote.
