2.3 Section Exercises
Verbal
1. What role does the horizontal asymptote of an exponential function play in telling us about the end behavior of the graph?
2. What is the advantage of knowing how to recognize transformations of the graph of a parent function algebraically?
Algebraic
3. The graph ofis reflected about the y-axis and stretched vertically by a factor ofWhat is the equation of the new function,State its y-intercept, domain, and range.
4. The graph ofis reflected about the y-axis and compressed vertically by a factor ofWhat is the equation of the new function,State its y-intercept, domain, and range.
5. The graph ofis reflected about the x-axis and shifted upwardunits. What is the equation of the new function,State its y-intercept, domain, and range.
6. The graph ofis shifted rightunits, stretched vertically by a factor ofreflected about the x-axis, and then shifted downwardunits. What is the equation of the new function,State its y-intercept (to the nearest thousandth), domain, and range.
7. The graph of is shifted leftunits, stretched vertically by a factor ofreflected about the x-axis, and then shifted downwardunits. What is the equation of the new function,State its y-intercept, domain, and range.
Graphical
For the following exercises, graph the function and its reflection about the y-axis on the same axes, and give the y-intercept.
8.
9.
10.
For the following exercises, graph each set of functions on the same axes.
11. and
12. and
For the following exercises, match each function with one of the graphs in (Figure).

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18.
For the following exercises, use the graphs shown in (Figure). All have the form

19. Which graph has the largest value for
20. Which graph has the smallest value for
21. Which graph has the largest value for
22. Which graph has the smallest value for
For the following exercises, graph the function and its reflection about the x-axis on the same axes.
23.
24.
25.
For the following exercises, graph the transformation ofGive the horizontal asymptote, the domain, and the range.
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28.
For the following exercises, describe the end behavior of the graphs of the functions.
29.
30.
31.
For the following exercises, start with the graph ofThen write a function that results from the given transformation.
32. Shift 4 units upward
33. Shift3 units downward
34. Shift2 units left
35. Shift5 units right
36. Reflectabout the x-axis
37. Reflectabout the y-axis
For the following exercises, each graph is a transformation ofWrite an equation describing the transformation.
38.
39.
40.
For the following exercises, find an exponential equation for the graph.
41.
42.
Numeric
For the following exercises, evaluate the exponential functions for the indicated value of
43. for
44. for
45. for
Technology
For the following exercises, use a graphing calculator to approximate the solutions of the equation. Round to the nearest thousandth.
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47.
48.
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51.
Extensions
52. Explore and discuss the graphs ofandThen make a conjecture about the relationship between the graphs of the functionsandfor any real number
53. Prove the conjecture made in the previous exercise.
54. Explore and discuss the graphs ofandThen make a conjecture about the relationship between the graphs of the functionsandfor any real number n and real number
55. Prove the conjecture made in the previous exercises.