## Friday, December 22, 2006

### Precalculus 3.1a notes - Exponential functions

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 ;

y-intercept (0,1);

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)