4.5E: Graphs of Logarithmic Functions (Exercises)
section 4.5 exercise
For each function, find the domain and the vertical asymptote.
1. \(f\left(x\right)=\log \left(x-5\right)\)
2. \(f\left(x\right)=\log \left(x+2\right)\)
3. \(f\left(x\right)=\ln \left(3-x\right)\)
4. \(f\left(x\right)=\ln \left(5-x\right)\)
5. \(f\left(x\right)=\log \left(3x+1\right)\)
6. \(f\left(x\right)=\log \left(2x+5\right)\)
7. \(f\left(x\right)=3\log \left(-x\right)+2\)
8. \(f\left(x\right)=2\log \left(-x\right)+1\)
Sketch a graph of each pair of functions.
9. \(f\left(x\right)=\log \left(x\right),\; g\left(x\right)=\ln \left(x\right)\)
10. \(f\left(x\right)=\log _{2} (x),\; g\left(x\right)=\log _{4} \left(x\right)\)
Sketch each transformation.
11. \(f\left(x\right)=2\log \left(x\right)\)
12. \(f\left(x\right)=3\ln \left(x\right)\)
13. \(f\left(x\right)=\ln \left(-x\right)\)
14. \(f\left(x\right)=-\log \left(x\right)\)
15. \(f\left(x\right)=\log _{2} (x+2)\)
16. f\left(x\right)=\log _{3} \left(x+4\right)\]
Find a formula for the transformed logarithm graph shown.
17. 18.
19. 20.
Find a formula for the transformed logarithm graph shown.
21. 22.
23. 24.
- Answer
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1. Domain: \(x > 5\) V. A. @ \(x = 5\)
3. Domain: \(x < 5\) V. A. @ \(x = 3\)
5. Domain: \(x > -\dfrac{1}{3}\) V. A. @ \(x = -\dfrac{1}{3}\)
7. Domain: \(x < 0\) V. A. @ \(x = 0\)
9.
11.
13.
15.
17. \(y = \dfrac{1}{\text{log}(2)} \text{log} (-(x - 1))\)
19. \(y = -\dfrac{3}{\text{log}(3)} \text{log}(x + 4)\)
21. \(y = \dfrac{3}{\text{log}(4)} \text{log}(x + 2)\)
23. \(y = -\dfrac{2}{\text{log}(5)} \text{log}(-(x - 5))\)