4.5E: Graphs of Logarithmic Functions (Exercises)

Section 4.5 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.

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Find a formula for the transformed logarithm graph shown.

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Section 4.6 Exponential and Logarithmic Models