Exponential Function
Graphs of f (x) = a x with a > 1 look like:
f (x) = 2
x
Graphs of f (x) = a x with 0<a <1 look like:
! 1$ x
f (x) = # &
" 2%
an increasing function
a decreasing function
Contains the point ( 0 , 1 )
horizontal asymptote y = 0
domain ( - ∞ , ∞ ) and range ( 0 , ∞ )
Logarithmic Function
Graphs of f (x) = log a x with a > 1 look like:
f (x) = log 2 x
Graphs of f (x) = log a x with 0<a <1 look like:
f ( x) = log 1 x
2
an increasing function
a decreasing function
Contains the point ( 1 , 0 )
vertical asymptote x = 0
range ( - ∞ , ∞ ) and domain ( 0 , ∞ )