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Mathematics LibreTexts

4.5E: Graphs of Logarithmic Functions (Exercises)

  • Page ID
    13909
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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.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

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