3.1a Exponential Functions and logarithmic functions are examples of transcendental functions.
The exponential function f with base a is denoted by
f(x) = ax
where a > 0, a not equal to 1, and x is any real number.
Examples: a0 = 1 any number to the zero power is one, why?
42/42 = 42-2 = 40= 1
Graphs of Exponential Functions - the domain, like those of polynomial functions, is the set of all real numbers.
f(x) = ax , a > 1
g(x) = a-x , a > 1
Domain: all reals;
Range: y > 0 ;
Asymptote y = 0
both graphs are continuous
Plot each graph and see the differences:
f(x) = ax , the graph is increasing
g(x) = a-x, the graph is decreasing
Transformations of Graphs of Exponential Functions:
a. f(x) = ax-h + k
Basic graph h = ________ k = ________ a = __________
b. f(x) = 2x-2 This is the graph shifted ___ units to the ________.
c. f(x) = 2x+3 This is the graph shifted ___ units to the________.
d. f(x) = 2x + 5, This is the graph shifted _____ units _____.
e. f(x) = 2-x This is the graph reflected in the _____.
f. f(x) = -2x This is the graph reflected in the _____.
Homework #25 pg. 225; #1-33 (odd)