# OSU MTH 111 - Act-#13 Composition-Key (5 pages)

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## Act-#13 Composition-Key

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- School:
- Oregon State University
- Course:
- Mth 111 - College Algebra

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Composition of Functions Math 111 Name GrpAct 13 Sect 12 4 16 Prerequisite Skills Evaluating functions Determining Domain Range Graphing a function point wise Key Terms Composition of functions Inside function Outside function Learning Objectives Use composition of functions to model multistep processes Compose functions defined numerically graphically and symbolically Interpret the meaning of the output of composed functions Determine the domain of a composition of functions 1 In the United States temperature is commonly measured in degrees Fahrenheit However in most sciences temperature 5 F 32 accepts an input of temperature in degrees Fahrenheit 9 and outputs the corresponding temperature in degrees Celsius The function K C C 273 accepts a temperature is measured in Celsius or Kelvin The function C F measured in Celsius and outputs the corresponding temperature measured in Kelvin a Use the formulas above to complete the following temperature conversion tables Fahrenheit Celsius Celsius Kelvin 13 25 25 248 5 15 10 263 32 0 0 273 41 5 15 288 59 15 25 298 77 25 40 313 b Fill out the table below converting temperatures directly from Fahrenheit to Kelvin Fahrenheit Kelvin 13 248 32 273 41 278 77 298 104 313 122 323 c Give a formula for a function that will accept an input of temperature in degrees Fahrenheit and will output the corresponding temperature in Kelvin The function you created in part c is the composition of the functions C and K and is written as 5 5 2297 K C F C F 273 F 32 273 F 9 9 9 This is read K composed with C of F or K of C of F In a composition the output of a function becomes the input of another function see the diagram in the box below d Use the formula you found in part c to determine K C 50 and explain what this represents Include units 5 2297 250 2297 2547 50 283 K 9 9 9 9 5 5 K C 50 50 32 273 18 273 10 273 283 K 9 9 K C 50 K C 50 OR A Composition of Functions The diagram below illustrates the composition K C F K C F original input fnt output input ftn final output C F F C C F K K Temp in Fahrenheit Temp in Celsius Check Your Work You should get K C 50 283 Make sure to fully explain what this represents Temp in Kelvin 2 The functions f and g are graphed below The function f accepts as input a UV index and outputs the time it takes for the skin of an average person to begin showing damage from sunburn The function g accepts as input the time of day measured as hours after 6 am and outputs the UV index for a typical spring day in Waikiki HI f 7 12 a Find and interpret f 7 Include units This means that when the UV index is 7 it

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