4.2E: Graphs of Exponential Functions (Exercises)
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Section 4.2 Exercises
Match each function with one of the graphs below.
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\(f\left(x\right)=2\left(0.69\right)^{x}\)
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\(f\left(x\right)=2\left(1.28\right)^{x}\)
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\(f\left(x\right)=2\left(0.81\right)^{x}\)
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\(f\left(x\right)=4\left(1.28\right)^{x}\)
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\(f\left(x\right)=2\left(1.59\right)^{x}\)
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\(f\left(x\right)=4\left(0.69\right)^{x}\)
If all the graphs to the right have equations with form \(f\left(x\right)=ab^{x}\),
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Which graph has the largest value for b?
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Which graph has the smallest value for b?
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Which graph has the largest value for a?
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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
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Shifting \(f(x)\) 4 units upwards
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Shifting \(f(x)\) 3 units downwards
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Shifting \(f(x)\) 2 units left
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Shifting \(f(x)\) 5 units right
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Reflecting \(f(x)\) about the x-axis
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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. 30.
31. 32.
Find an equation for the exponential function graphed.
33. 34.
35. 36.
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Section 4.3 Logarithmic Functions