Math question?

Question

g(x)=log[base2](-x-3)-2 using transformation of f(x)=log[base2]x. What are the coordinates of the asymptote?

What are the x intercept (s)

What is the y intercept

list three coordinate points

Answer 1

asymptote is at -3

x intercept is at -7

y intercept is at there is no y intercept, y isnt defined when x=0

coords (-7,0) (-4,-2) (-5, -1)

Answer 2

normal vertical asymptote for log x is x=0, so for log (x+3) it will be x = -3.

normal x intercept is (1,0), transformed 3 left and then reflected over x=-3 would make it (-4,0), but we have a shift 2 down as well, and for the function to rise 2, x will have to "increase" 3, which make the intercept (-7,0). there's a point where trying to follow all the changes relative to the standard reference points gets tedious, and it's simpler to do a little arithmetic:

log[2](-x-3)-2 = 0
log[2](-x-3) = 2
-x-3 = 4
-x = 7
x = -7

y intercept:

log[2](-0-3) - 2 =
but can't do log of negative, so no intercept. after all, log x goes up and right from vertical asymptote. reflected function should go up and left, and since translated asymptote is x=-3, no crossing of y axis.

one more point besides (-7,0) and (-4,-2)? (-5,-1)