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1.5 Combintions of Functions

1.5 Combintions of Functions. Students will be able to: - add, subtract, multiply, and divide functions. - find compositions of one function with another. - Use combinations of two functions to model and solve real-life problems. Sum, Difference, Product, and Quotient of Function.

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1.5 Combintions of Functions

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  1. 1.5 Combintions of Functions Students will be able to: - add, subtract, multiply, and divide functions. - find compositions of one function with another. - Use combinations of two functions to model and solve real-life problems.

  2. Sum, Difference, Product, and Quotient of Function Sum: (f+g)(x) = f(x) + g(x) Difference: (f-g)(x) = f(x) – g(x) Product: (fg)(x) = f(x)•g(x) Quotient:

  3. Example 1: Given and , find . Then evaluate the sum when x = 2.

  4. Example 2: Given and , find (f – g)(x). Then evaluate the difference when x = 2.

  5. Example 3 Given and , find (fg)(x). Then evaluate the product when x = 4.

  6. Example 4: Find (f/g)(x) and (g/f)(x) for the functions given by and . Then find the domains of each.

  7. Example 5: Find for , . If possible, find and .

  8. Example 6: Given f(x) = x + 2 and , evaluate (a) and (b) when x = 0,1,2, and 3.

  9. Example 7: Find the domain of the composition for the functions given by and .

  10. Example 8: Given and , find each composition. a. b.

  11. Example 9: Write the function as a composition of two functions.

  12. Example 10: Write the function as a composition of two functions.

  13. Composition of Functions: Convert miles to inches.

  14. Example F(x) displays the percent increase in UV radiation when the ozone layer thins by x% G(x) displays the percent increases in cases of skin cancer given the % increase in UV radiation G(F(2) = Describe what G(F(x)) computes.

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