4.2E: Graphs of Exponential Functions (Exercises)

Section 4.2 Exercises

 

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

If 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. 30.

31. 32.

Find an equation for the exponential function graphed.

33. 34.

35. 36. \[289\]

Section 4.3 Logarithmic Functions