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Combining Functions

Combining Functions . Section 1.7. Objectives. Determine the domain and range (where possible) of a function given as an equation. Add, subtract, multiply, and/or divide function. State the domain two function combined in an arithmetic method.

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Combining Functions

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  1. Combining Functions Section 1.7

  2. Objectives • Determine the domain and range (where possible) of a function given as an equation. • Add, subtract, multiply, and/or divide function. • State the domain two function combined in an arithmetic method. • Put together two (or more) functions using composition. • Determine the value of the composition of two (or more) functions given the graphs of the functions. • Determine the value of the composition of two (or more) function given the equations of the functions. • State the domain two function combined through composition.

  3. Objectives • Decompose the composition of two functions into it constituent functions. • Solve a word problem involving the composition of functions.

  4. Vocabulary • domain • range • function composition

  5. Domain Questions • Does the function have a denominator? • Does the function have a square or even root? • Does the function have a log or ln in it? • Did the function arise from finding an inverse? • Is this a “real world” problem?

  6. Find the domain of the function:

  7. Find the domain of the function:

  8. Find the domain of the function:

  9. Find the domain of the function:

  10. Given the functions and find each of the following:

  11. Given the functions and find the domain of each of the following:

  12. For the functions f(x) and g(x) are given in the graph below.  Find the indicated corresponding function values

  13. Given the functions and find each of each of the following:

  14. Given the functions and find each of the following:

  15. Given the functions and find the domain of each of the following:

  16. For the functions f(x) and g(x) are given in the graph below.  Find the indicated corresponding function values

  17. Express the function in the form . If ,find g(x).

  18. A spherical weather balloon is being inflated. The radius of the balloon is increasing at the rate of 9 cm per second. Express the surface area of the balloon as a function of time t (in seconds).

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