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):
|
y = 4loge (3x - 2) - 4 | |
21. | 22. | |
23. | 23. | |
Miscellaneous graphing problems. | 25. (i) Draw the graphs of both (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.