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. |
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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.