Dr. J's Maths.com
Where the techniques of Maths
are explained in simple terms.

Functions - Logarithmic - Graphing Log functions.
Test Yourself 2.


 

The graph questions are separated into the following categories:
Vertical shift
Expansion/contraction
Transformation - combination
Horizontal shift
Combination of transformations
Miscellaneous graphing problems

Graph each of the following functions marking in all relevant information.

Vertical shift 1.  
Expansion/contraction 3.  
  5.  
Horizontal shift 7.  
  9.  
Combination of transformations 11. y = loge (x - 4) y = 2loge (9 + 3x)
  13. y = 3 loge (2 - x) y = 5loge (5 - 2x)
  15.  
  17.  
 

19. For the equation loge y = xloge (0.5):

(i) write an equation for y = f(x).

(ii) Hence sketch the graph of y = f(x).

 y = 4loge (3x - 2) - 4
  21. 22.
  23. 23.
Miscellaneous graphing problems.

25. (i) Draw the graphs of both
y = 2 ln x and y = ln (5x - 6).

(ii) Solve the two equations simultaneously and show why your point of intersection is approximately reflected in your graph.

26. (i) Sketch y = ln x.

(ii) By drawing a second sketch of a relevant curve on your first set of axes, find the number of solutions for the equation y = ln x - x = -2.
  27. Sketch the graph of y = x - ln x. 28.

 

To expand your understanding of the graphing techniques required for advanced graphs, use some graphing software such as Desmos or Geogebra.