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Mathematics LibreTexts

4.5E: Graphs of Logarithmic Functions (Exercises)

  • Page ID
    13909
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    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.png18. 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.png20. 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.png22.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.png24.屏幕快照 2019-06-26 下午6.30.01.png