Parent function of logarithmic graph y = logax a > 1 0 < 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.

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.

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 +1 +2 +1 +2 +1 (2,2) (4,3) x = 1

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 -3 -3 -3 (-2,0) (-2 ½ ,1). x = -3

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