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 \(f\left(x\right)=ab^{x}\),

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.  30. 

31.  32. 

Find an equation for the exponential function graphed.

33.  34. 

35.  36.