Logarithmic Graphs


Domain: (0,∞) Domain: (0,∞)
Range: (-∞,∞) Domain: (-∞,∞)
X-intercept: (1,0) x-intercept: (1,0)
Y-intercept: none y-intercept: none
Asymptote: y-axis Asymptote: y-axis

Transormations from y=\log_b(x)

k(x)=\log(x-h) Move right h units
k(x)=\log(x+h) Move left h units
m(x)=-\log(x) Reflect across x-axis
h(x)=\log(x)+k Move up K units
h(x)=\log(x)-k Move down k units
p(x)=b\cdot\log(x) Expand vertically by a factor of b

Example Describe the transformation of g(x)=2\log(x)+5 from f(x)=\log(x) and graph.

Negative in front: reflect across x-axis
2: expand vertically by a factor of 2
+5: move up 5 units