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

Functions - Logarithmic - Graphing Log functions.
Test Yourself 1.


 

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. y = logex + 3 2. y = logex - 4 
Expansion/contraction 3. y = 4loge x  4. y = -2loge x 
  5. y = 2 ln 3x
Hint.As we have 3x not x after the log, put 3x = 1 to reflect the basic log graph having an x intercept = 1.
Then solve for the new intercept.		 6.
Hint.Rewrite the log expression to express to a power of a half.
Then use a log law to bring the index to the front.
Transformation - combination 7. y = 3ln x - 4 8. y = 3 + 4ln x
  9. y = 2 - 2log3 x 10. y = 5 + 4 loge x
Horizontal shift 11. y = loge (3x + 2) 12. y = 2 loge (x + 4)
  13. y = loge (5 + 2x) 14. y = 2loge (9 + 3x)
  15. y = 3 loge (x - 4) 16. y = 3 loge (2 - x)
  17. y = 5 loge (5 - x) 18. y = 2 loge (1 - 2x )
Combination of transformations 19. y = 2loge (x+1) + 3 20. y = 4loge (3x - 2) - 4
 

21. y = log10 (x + 2) + 2

Also state its domain and range.

 22. y = 3 ln (1 - x) + 1
Miscellaneous graphing problems. 23. (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.

 24. (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.
 

25. State the domain and range of the function .

 26. Draw the graph of
y = log |x|.

 

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