
# 4.2.2E: Graphs of Exponential Functions (Exercises)


Section 4.2 Exercise

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

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

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.

1. B

3. A

5. E

7. D

9. C

11.

13.

15.

17. $$y = 4^x + 4$$

19. $$y = 4^{x + 2}$$

21. $$y = -4^x$$

23. As $$x \to \infty$$, $$f(x) \to -\infty$$. As $$x \to -\infty$$ $$f(x) \to -1$$

25. As $$x \to \infty$$, $$f(x) \to -2$$. As $$x \to -\infty$$ $$f(x) \to \infty$$

27. As $$x \to \infty$$, $$f(x) \to 2$$. As $$x \to -\infty$$ $$f(x) \to \infty$$

29. $$y = -2^{x + 2} + 1 = -4(2)^x + 1$$

31. $$y = -2(2)^{-x} + 3$$

33. $$y = -2(3)^x + 7$$

35. $$y = 2(\dfrac{1}{2})^x - 4$$