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Graphing Exponential Functions

Graphs HOME | Achievement Objectives | Parabola Graphs | Parabola Questions | Cubics | Hyperbola | Circles | Exponential | Logs | Radians | Trig Graphs Overview | Trig Vertical Shift | Trig Horizontal Shift | Trig Equations | Trig Models | General Translations | Applications | Revision

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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)

Class notes, Blank notes

Ex12.01, Ex12.02, Ex12.03

Exponential

p51,

GeoGebra Java Exponential

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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 | Daves Notes

Ex12.04, Ex12.05

Exponential

p52,

GeoGebra Java Exponential Translation

9



Even More Exponential

Practice sketching translated exponential functions and exponential applications

Exponential Graphs

Class notes, Blank notes

Ex12.05

Exponential

Jump down to... Basic exponential | exponential family | inverted & reflected exponential | vertical shift | horizontal shift | combined shifts

Basic exponential

Exponential rule

x y
3 8
2 4
1 2
0 1
-1 1/2
-2 1/4
-3 1/8

Graph Key features

Note: the x axis is an asymptote
The graph passes through the point (0,1)
y intercept y = 1
 

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Exponential family


The number changing is the BASE

x is the exponent (power)

Mouse-over the equations to see the graph translation

Neote: the x axis is an asymptote
All graphs pass through the point (0,1)
Look for the y value when x = 1

Animation of exponential graphs

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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

 

   The graph is reflected in the horizontal asymptote

   The graph is reflected in the y axis

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Vertical shift

Adding a constant vertically translates the exponential graph
 

 

Mouse-over the equations to see the graph translation

Note: The asymptote is translated vertically
The y intercept is 1 unit above the asymptote

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Horizontal shift

Adding a constant to x horizontally translates the parabola graph
 

 

Mouse-over the equations to see the graph translation

Note: The point (0,1) indicates the horizontal translation

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Combined shifts

Horizontal and vertical shifts can be combined
 

 

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

Explanation

Explanation

Explanation

Note: Look for a vertical shift, then a horizontal shift, then find the base number

Excel demo (contains macros)

 

Continue to logarithmic graphs

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