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Building Functions from Functions

Building Functions from Functions. A Presentation By: Michael Cronce , Zac Frye, and Shane Yach. Combining Functions Algebraically: Example #1. Find formulas for the functions , , and , and then give the domain of each. ; ( = ; domain: (-∞, ∞) = ; domain: (-∞, ∞ )

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Building Functions from Functions

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  1. Building Functions from Functions A Presentation By: Michael Cronce, Zac Frye, and Shane Yach

  2. Combining Functions Algebraically: Example #1 • Find formulas for the functions , , and , and then give the domain of each. • ; • ( = ; domain: (-∞, ∞) • = ; domain: (-∞, ∞) • = ; domain: (-∞, ∞)

  3. Combining Functions Algebraically: Example #2 • Find formulas for the functions , , and , and then give the domain of each. • ; • =; domain: [0, ∞) • = ; domain: [0, ∞) • = sin x; domain: [0, ∞)

  4. Combining Functions Algebraically: Example #3 • Find formulas for and , and then give the domain of each. • ; • = ; and ; domain: [-3, 0) (0, ∞) • = ; ; domain: (-3, ∞)

  5. Combining Functions Algebraically: Example #4 • Find formulas for and , and then give the domain of each. • ; • = ; ; domain: (-1, 1) • = ; and ; domain: [-1, 0) (0, 1]

  6. Composition of Functions: Example #1 • Find and . • ; • = = = = = 5 • = = = = = -6

  7. Composition of Functions: Example #2 • Find and . • ; • = = = = 8 • = = = = = = 3

  8. Composition of Functions: Example #3 • Find and , and then give the domain of each. • ; • = = = ; domain: (-∞, ∞) • = = = ; domain: (-∞, ∞)

  9. Composition of Functions: Example #4 • Find and , and then give the domain of each. • ; • = = = ; domain: [-1, ∞) • = = ; domain: (-∞, -1] [1, ∞)

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