Denise's Bicycle Trip Problem Denise took a bicycle ride away from her home today. She left home at 12 a.m. and arrived back at home at 8 pm. The graph shown in figure 1 represents Denise's distance from home during her ride.

Let the function d t represent Denise's distance in miles from home during her trip in terms of the time in hours. The graph shown in figure 2 is a transformation of the function d t shown in figure 1.

Example a : Explain the real-world meaning of this transformation. Answer a: The graph has been translated 3 units to the right. Denise started her trip 3 hours later (3 p.m.) and arrived home 3 hours later (12 p.m.). Example b: Use function notation to represent this transformation. Answer b: d t 3 Transfer the graph of the function d t ,shown in figure 1, to your paper. Use the graph to help you answer parts a and b for each of the transformations of the function d t graphed in problems 1 - 5.

Fish in a Lake Problem Daniel has a lake in his backyard. He plans to raise fish in his lake. He released 100 fish in his lake in 1996. The graph in figure 9 represents the number of fish in Daniel's lake in terms of the number of years since 1996.

Let the function f t represent the number of fish in Daniel's lake in terms of the number of years since 1996. Transfer the graph of the function f t to your paper. Use this graph to help you answer problems 7 - 13.

Explain the meaning of the transformation of the function f t shown in figure 10 in the context of this problem then use function notation to represent this transformation. Daniel released the fish in 1998. f t 2

Explain the meaning of the transformation of the function f t shown in figure 11 in the context of this problem then use function notation to represent this transformation. Daniel released the fish in 1992. f t 4

Explain the meaning of the transformation of the function f t shown in figure 12 in the context of this problem then use function notation to represent this transformation. Daniel released 100 more fish into the pond in 1996 which increased the number of fish in the pond each year by 100 more fish. f t 1

Explain the meaning of the transformation of the function f t shown in figure 13 in the context of this problem then use function notation to represent this transformation. The fish population increased the same amount as the population in 3.5 years which is 1/2 the time as the function shown in figure 9. f 2 t

Explain the meaning of the transformation of the function f t shown in figure 14 in the context of this problem then use function notation to represent this transformation. The fish population increased by 1/2 as much as the fish population shown in figure 9. 1 2 f t

Use function notation to represent the transformation of the function f t shown in figure 15. f t

Use function notation to represent the transformation(s) of the function f t shown in figure 16. (Hint: You may need to use more than one transformation.) f t 13

Transformations of Functions Exploration Modules After you have completed this lesson you can continue to explore transformations of functions by choosing a module listed below. Go to Transformation of Functions Exploration Module Go to Transformation of Functions (Graphically) Module Go to Transformation of Functions using a Graphing Calculator Module