# Graphing Exponential Functions

 Exponential Functions Sketching Basic exponential functions y = Ax Vertical and horizontal translations of the exponential functions y = ABx+C + D Remember to define the Domain if you write the equation for part of a Exponential graph. Exponential Graphs with slider bar transformations (allow macros)   Ex12.01, Ex12.02, Ex12.03 Exponential p51, GeoGebra Java Exponential More Exponential Practice sketching stretched and translated exponential functions Find the equation when given a graph Applications of and exponential applications Exponential Graphs  Class notes, Blank notes Ex12.04, Ex12.05 Exponential p52, GeoGebra Java Exponential Translation Even More Exponential Practice sketching translated exponential functions and exponential applications Exponential Graphs  Ex12.05 Exponential

# Basic exponential

Exponential rule x y
3 8
2 4
1 2
0 1
-1 1/2
-2 1/4
-3 1/8 # Exponential family  The number changing is the BASE

x is the exponent (power)

#### Mouse-over the equations to see the graph translation     # Inverted & reflected exponential

A negative multiplier inverts the graph

A negative x reflects in the y axis

#### Mouse-over the equations to see the graph translation    # Vertical shift

Adding a constant vertically translates the exponential graph

#### Mouse-over the equations to see the graph translation     # Horizontal shift

Adding a constant to x horizontally translates the parabola graph

#### Mouse-over the equations to see the graph translation     # Combined shifts

Horizontal and vertical shifts can be combined

#### Mouse-over the equations and key words to see the graph   Explanation Explanation Explanation