Ex algebra (5)

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Ex algebra (5)

  1. 1. Lista 2 de C´lculo I a 2010-2 3 UFES - Universidade Federal do Esp´ ırito Santo Opera¸˜es com fun¸˜es co co DMAT - Departamento de Matem´tica a Fun¸˜o composta ca LISTA 2 - 2010-2 Transforma¸˜es em gr´ficos co a 1 1. Se f (x) = 3x2 + 2 e g(x) = , determine: 3x + 2 (a) (f + g)(x) (c) (f · g)(x) g (e) (x) f f (b) (f (x))−1 (d) (x) (f) (f ◦ g)(x) g 3−x 2. Seja f (x) = . Determine: x (a) f x2 − (f (x))2 1 1 (c) (f ◦ f )(x) (b) f − x f (x) 1 −x , x < 0 , x<0 (a) (f ◦ g)(x) 3. Dadas f (x) = e g(x) = √x , determine: x2 , x ≥ 0 x , x≥0 (b) (g ◦ f )(x) Nos exerc´ ıcios 4. a 11., a partir do gr´fico da fun¸˜o y = f (x) dado abaixo, esboce o gr´fico da a ca a fun¸˜o dada. ca y = f(x) 4. y = f (|x|) 8. y = f (x + 2) 4 2 9. y = f (x) + 3 5. y = |f (x)| –8 –6 –4 –2 0 2 4 6 8 10 12 14 x f (x) + |f (x)| –2 10. y = –4 6. y = f (−x) 2 f (x) − |f (x)| 7. y = −f (x) 11. y = 2 Esboce os gr´ficos das fun¸˜es dos exerc´ a co ıcios 12. a 17. 12. f (x) = 8 − 3 x 2 −1 14. f (x) = |x − 1|3 16. f (x) = (|x| − 1)3 √ 13. f (x) = 2|x| − 6 15. f (x) = 1 + 3 1 − x 17. f (x) = x2 − 4|x| + 3 Nos exerc´ ıcios 18. a 21. determime o dom´ ınio, a imagem e esboce o gr´fico da fun¸˜o dada. a ca 18. f (x) = 3 sen (2πx) x 1 20. f (x) = sen − , 0 ≤ x ≤ 4π 2 2 x 1 π 19. f (x) = tan 21. f (x) = sec x − 2 2 3
  2. 2. Lista 2 de C´lculo I a 2010-2 4 RESPOSTAS 9x3 + 6x2 + 6x + 5 3 2 1. (a) y = ,x = − (d) y = 9x3 + 6x2 + 6x + 4, x = − 3x + 2 2 3 1 1 2 (b) y = 2 (e) y = 3 ,x = − 3x + 2 9x + 6x2 + 6x + 4 3 3x2 + 2 2 18x2 + 24x + 11 2 (c) y = ,x = − (f) y = ,x = − 3x + 2 3 9x2 + 12x + 4 3 6x − 2x2 − 6 2 9x − 3x − 3 4x − 3 2. (a) y = (b) y = (c) y = x2 3−x 3−x √ 1 −x , x < 0 − , x<0 (b) (g ◦ f )(x) = 3. (a) (f ◦ g)(x) = x x , x≥0 x , x≥0 4. 7. 10. y y y 4 4 4 2 2 2 x x x –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –2 –2 –2 –4 –4 –4 5. 8. 11. y y y 4 4 4 2 2 2 x x –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 x –2 –2 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –2 –4 –4 –4 6. 9. y y 4 6 2 4 x 2 –14 –10 –8 –6 –4 –2 2 4 6 8 10 12 14 –2 x –14 –10 –8 –6 –4 –2 0 2 4 6 8 10 12 14 –4 –2 12. 14. 16. y y y 8 2 2 6 1 4 1 x 2 x –4 –3 –2 –1 1 2 3 4 10 20 x –2 2 4 –1 –2 13. 15. 17. y 8 y y 2 6 4 4 x 0 2 2 –4 –2 2 4 6 x x –10 –8 –6 –4 –2 0 2 4 6 8 10 –2 –6 –4 –2 2 4 6 18. 20. y 3 2 2 1 –6 –4 –2 0 2 4 x6 0 x 5 10 –2 19. 21. y y 10 10 5 x x –10 10 –15 –10 –5 5 10 15 –5 –10 –10

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