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

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