4.5E: Graphs of Logarithmic Functions (Exercises)

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Jan 2, 2021
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- 4.5: Graphs of Logarithmic Functions
- 4.6: Exponential and Logarithmic Models

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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. $屏幕快照 2019-06-26 下午6.26.37.png$ 18. $屏幕快照 2019-06-26 下午6.28.07.png$

19. $屏幕快照 2019-06-26 下午6.28.25.png$ 20. $屏幕快照 2019-06-26 下午6.28.40.png$

Find a formula for the transformed logarithm graph shown.

21. $屏幕快照 2019-06-26 下午6.29.08.png$ 22. $屏幕快照 2019-06-26 下午6.29.26.png$

23. $屏幕快照 2019-06-26 下午6.29.43.png$ 24. $屏幕快照 2019-06-26 下午6.30.01.png$

Answer

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. $Screen Shot 2019-10-04 at 2.47.23 PM.png$

11. $Screen Shot 2019-10-04 at 2.47.40 PM.png$

13. $Screen Shot 2019-10-04 at 2.47.56 PM.png$

15. $Screen Shot 2019-10-04 at 2.48.16 PM.png$

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. $y = -\dfrac{2}{\text{log}(5)} \text{log}(-(x - 5))$

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