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Mathematics LibreTexts

4.2E: Graphs of Exponential Functions (Exercises)

  • Page ID
    13906
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    Section 4.2 Exercises

    Match each function with one of the graphs below.

    屏幕快照 2019-06-24 下午10.50.10.png

    1. \(f\left(x\right)=2\left(0.69\right)^{x}\)
    2. \(f\left(x\right)=2\left(1.28\right)^{x}\)
    3. \(f\left(x\right)=2\left(0.81\right)^{x}\)
    4. \(f\left(x\right)=4\left(1.28\right)^{x}\)
    5. \(f\left(x\right)=2\left(1.59\right)^{x}\)
    6. \(f\left(x\right)=4\left(0.69\right)^{x}\)

    If all the graphs to the right have equations with form \(f\left(x\right)=ab^{x}\),

    屏幕快照 2019-06-24 下午10.51.30.png

    7. Which graph has the largest value for \(b\)?
    8. Which graph has the smallest value for \(b\)?
    9. Which graph has the largest value for \(a\)?
    10. Which graph has the smallest value for \(a\)?

    Sketch a graph of each of the following transformations of \(f\left(x\right)=2^{x}\)

    11. \(f\left(x\right)=2^{-x}\)

    12. \(g\left(x\right)=-2^{x}\) 

    13. \(h\left(x\right)=2^{x} +3\)

    14. \(f\left(x\right)=2^{x} -4\) 

    15. \(f\left(x\right)=2^{x-2}\)

    16. \(k\left(x\right)=2^{x-3}\)

    Starting with the graph of \(f\left(x\right)=4^{x}\), find a formula for the function that results from

    17. Shifting \(f(x)\) 4 units upwards

    18. Shifting \(f(x)\) 3 units downwards

    19. Shifting \(f(x)\) 2 units left

    20. Shifting \(f(x)\) 5 units right

    21. Reflecting \(f(x)\) about the x-axis

    22. Reflecting \(f(x)\) about the y-axis

    Describe the long run behavior, as \(x \to \infty\) and \(x \to -\infty\) of each function

    23. \(f\left(x\right)=-5\left(4^{x} \right)-1\)

    24. \(f\left(x\right)=-2\left(3^{x} \right)+2\) 

    25. \(f\left(x\right)=3\left(\frac{1}{2} \right)^{x} -2\)

    26. \(f\left(x\right)=4\left(\frac{1}{4} \right)^{x} +1\) 

    27. \(f\left(x\right)=3\left(4\right)^{-x} +2\)

    28. \(f\left(x\right)=-2\left(3\right)^{-x} -1\)

    Find a formula for each function graphed as a transformation of \(f\left(x\right)=2^{x}\).

    29.  屏幕快照 2019-06-24 下午10.55.00.png30. 屏幕快照 2019-06-24 下午10.55.16.png

    31.  屏幕快照 2019-06-24 下午10.55.36.png32. 屏幕快照 2019-06-24 下午10.55.55.png

    Find an equation for the exponential function graphed.

    33. 屏幕快照 2019-06-24 下午10.56.14.png 34. 屏幕快照 2019-06-24 下午10.56.29.png

    35.  屏幕快照 2019-06-24 下午10.57.12.png36.  屏幕快照 2019-06-24 下午10.57.36.png