1. Parent function of logarithmic graph y = logax
a > < a < 1
Properties:
Domain is (0,∞) Range is (-∞,∞)
The x intercept of the graph is (1,0)
There is no y intercept vertical asymptote at x = 0
The graph is increasing if a > 0 and decreasing if 0 < a < 1
Contains the points (1/a, -1), (1,0), (a,1) or (a,-1), (1,0), (1/a, 1)
The graph is smooth and continuous.

2. y = alogb(x-h)+ k
To be a logarithmic increase b must be greater than 1. If 0<b<1 then it is a logarithmic decrease
The a, h, and k do the same things as they always have. a stretches, h moves it left and right and k moves it up and down. This effects the asymptote and the critical point how?
Find 2 points usually whatever makes the log = 0 and 1. and the asymptote moves with h.

3. The vertical asymptote shifts right 1
The vertical asymptote shifts right 1. the critical point shifts right 1 and up 2.
y =log 3 (x-1)+2 a
(1,0). & (3,1) x = 0
(2,2) (4,3) x = 1

4. The vertical asymptote shifts left 3
The vertical asymptote shifts left 3. the critical point shifts left 3 as well and the graph is flipped since the base is between 0-1.
y =log 1/2 (x+3) a
(1,0). & ( ½ ,1) x = 0
(-2,0) (-2 ½ ,1). x = -3

5. 76) f(x) = -2ln(x+1)