Nayland College

Nayland College - Mathematics

Home . Year 9 . Year 10 . Level 1 . Level 2 . L3 Statistics . L3 Maths . L3 Calculus . About . Links

NZAMT NZQA NZ Grapher NZ Maths Census at School Study It Khan Academy Desmos

Graphing Log 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

10



Logarithmic Functions

Basic Log graphs with different bases, such as y = Log2(x)
How the base changes the graph shape
Relating the Log graph to the exponential graph

Remember to define the Domain if you write the equation for a Log graph.

Log graphs

Class notes, Blank notes

Ex12.07

Log Graphs

p54,

GeoGebra Java Log Translation

11



More Log Graphs

Vertical and horizontal translation of log graphs
Log and exponential applications

Log graphs

Class notes, Blank notes | Daves Notes

Log Graphs

Jump down to... Basic log graph | different basesinverted graph | vertical shift | horizontal shift | combined shifts

Basic log graph

The log graph is a reflection of an exponential graph in the line y = x

Mouse-over the equationsand key words

x y
3  
2  
1  
0  
-1  
-2  

Key features: no negative x values,
The y axis is a vertical asymptote
The log graph is the reflection of the exponential graph in the line y = x

back to top

 

 

 

Different bases

A different base changes the shape of the graph

 

 

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

y = log2x

Features

Features

Features

Key features: All graphs pass through point (1,0)
Note the y = 1 value

back to top

 

 

Inverted log graph

A negative multiplier inverts the graph about the x axis

 

 

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

y = log2x

 

Features

 

 

Key features: Inverted graph pass through point (1,0)

back to top

 

 

 

Vertical shift

Adding a constant vertically translates the log graph
 

 

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

y = log2x

 

Features

Features

Features

Key features: the point (1,0) is translated vertically
Vertical asymptote remains unchanged

back to top

 

 

 

Horizontal shift

Adding a constant to x horizontally translates the log graph
 

 

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

y = log2x

 


Features


Features


Features

Key features: the point (1,0) and the vertical asymptote translated sideways 

back to top

 

 

Combined shifts

Horizontal and vertical shifts can be combined
 

 

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

y = log2x

 


Features


Features


Features

The asymptote will give the horizontal shift
The point 1 unit from the asymptote will give the vertical shift
The base of the log?

Excel demo (contains macros)

 

Continue to points of intersection

back to top