4.5E: Graphs of Logarithmic Functions (Exercises)

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.