**3.1a Exponential Functions and logarithmic functions are examples of transcendental functions**.

The exponential function ** f** with base

**is denoted by**

*a*f(x) = a^{x }

where a > 0, a not equal to 1, and ** x** is any real number.

Examples: a^{0} = 1 any number to the zero power is one, why?

4^{2}/4^{2 }= 4^{2-2 }= 4^{0}= 1

**Graphs of Exponential Functions** - the domain, like those of polynomial functions, is the set of all real numbers.

*f*(*x*) = a^{x} , *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*) = a^{x} , **the graph is increasing**

*g*(*x*) = a^{-x}, *the graph is decreasing*

Transformations of Graphs of Exponential Functions:

a. f(x) = **a**^{x-h} + **k**

Basic graph **h** = ________ **k** = ________ **a** = __________

b. f(x) = 2^{x-2 }This is the graph shifted ___ units to the ________.

c. f(x) = 2^{x+3 }This is the graph shifted ___ units to the________.

d. f(x) = 2^{x} + 5, This is the graph shifted _____ units _____.

e. f(x) = 2^{-x }This is the graph reflected in the _____.

f. f(x) = **-**2^{x }This is the graph reflected in the _____.

Homework #25 pg. 225; #1-33 (odd)