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Mathematics LibreTexts

4.2E: Graphs of Exponential Functions (Exercises)

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    13906
  • [ "article:topic", "license:ccbysa", "showtoc:no", "authorname:lippmanrasmussen" ]

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    Section 4.2 Exercises

     

    imageMatch each function with one of the graphs below.

    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. \(f\left(x\right)=4\left(0.69\right)^{x}\)

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

    1. Which graph has the largest value for b?

    2. Which graph has the smallest value for b?

    3. Which graph has the largest value for a?

    4. 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

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

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

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

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

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

    6. 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. image 30. image

    31. image 32. image

    Find an equation for the exponential function graphed.

    33. image 34. image

    35. image 36. image \[289\]

    Section 4.3 Logarithmic Functions