Question

Write an equation for a log functions base 2 whose graph has the following properties:

vertical asymptote of x=-6
Domain of x<-6
Passing through (-8,3)

Answer 1

log_2(x) has asymptote at x=0, so

log_2(x+6) has its asymptote at x=-6
But, its domain is x > -6. So, we want

log_2(-x-6)

at x = -8, we have
log_2(8-6) = 1

So, we want

y = 3log_2(-x-6)