Mat funcoes  002 exercicios
Upcoming SlideShare
Loading in...5
×
 

Like this? Share it with your network

Share

Mat funcoes 002 exercicios

on

  • 1,320 views

 

Statistics

Views

Total Views
1,320
Views on SlideShare
1,320
Embed Views
0

Actions

Likes
0
Downloads
1
Comments
0

0 Embeds 0

No embeds

Accessibility

Categories

Upload Details

Uploaded via as Adobe PDF

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Mat funcoes 002 exercicios Document Transcript

  • 1. EXERCÍCIOS SOBRE FUNÇÕES1) Construa os gráficos das seguintes funções de R em R: a) y = x + 2 4 − 3x d) d) y = b) y = - x + 1 2 c) y = 2x e) y = -2x +32) Construa os gráficos das seguintes funções de R em R: a) y = 2x2 c) y = 4x – x2 b) y= - x2 +3x d) y = 2x2 - 10x + 73) Determine os valores de x que satisfazem a cada uma das expressões abaixo: a) 5 x − 3 = 12 1 d) x −3 < 2 b) 2 x − 3 = 7 x − 5 e) − 2x − 7 ≥ 3 3x + 8 c) =4 2x − 34) Construa os gráficos das seguintes funções: a) y = | x | +2 c) y = x2 - 4 b) y = | x +2| d) y = |x2 – 4|5) Construa os gráficos das seguintes funções: a) y = x c) y = x +3 b) y = x +3 d) y = 4 x6) Complete com verdadeiro ou falso, com x e y pertencentes aos reais.a) ( ) (x + y ) = x 2 + y 2 2 e) ( ) log 3 (x + y ) = log 3 x + log 3 y, x.y > 0 ) (x.y ) = x 2 .y 2 x y x+y 2b) ( f) ( ) + = , x.y ≠ 0 y x y+xc) ( ) x 2 + y2 = x + y g) ( ) x2 = xd) ( ) (x + y )2 =x+y7) Esboce o gráfico das seguintes funções: a) f(x) = 2x x 1  x d) f(x) =   - 3 1  2 b) g(x) =   2 e) g(x) = 3.2x c) h(x) = 2x + 2 x f) h(x) = 2
  • 2. 8) Determine o domínio e faça um esboço do gráfico da função dada. a) f (x ) = log 1 x c) f (x ) = ln( x + 1) e) f (x ) = log 1 (− x ) 4 2 d) f (x ) = ln( x − 2) b) f (x ) = log 2 x f) f (x ) = − log 1 x 39) Construa o gráfico (um período completo) das seguintes funções, explicitando o domínio, aimagem e o período:a) y = 3 sen x b) y = 2 - sen x  π xc) y = sen  x −  d) y = 2 sen  2 410) Calcule f o g( x ) , g o f ( x ) , f o f ( x ) e g o g ( x) para as seguintes funções:a) f ( x ) = x + 10 e g ( x) = sen ( x )b) f ( x ) = x 2 + 3x e g ( x ) = 2 x − 7 f (x + h ) − f (x )11) Simplifique a expressão onde ha) f ( x ) = x 2 − 3x 1b) f ( x ) = xc) f ( x ) = ( x + 2) 2
  • 3. RESPOSTAS DOS EXERCÍCIOS SOBRE FUNÇÕES1)y = X+2 4.0 y = -x+1 4.0 y = 2x 4.0 3.0 3.0 3.0 2.0 2.0 2.0 1.0 1.0 1.0 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 5.0 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 5.0 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 −1.0 −1.0 −1.0 −2.0 −2.0 −2.0 −3.0 −3.0 −3.0 −4.0 −4.0 −4.0y = (4-3x)/2 4.0 y = -2x+3 4.0 3.0 3.0 2.0 2.0 1.0 1.0 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 5.0 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 5.0 −1.0 −1.0 −2.0 −2.0 −3.0 −3.0 −4.0 −4.02)y = 2*x^2 4.0 y = -x^2+3x 4.0 y = 4x-x^2 4.0 y = 2x^2-10x+7 6.0 3.0 3.0 3.0 5.0 4.0 2.0 2.0 2.0 3.0 2.0 1.0 1.0 1.0 1.0 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 5.0 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 5.0 −4.0 −3.0 −2.0 −1.0 1.0 2.0 3.0 4.0 −6.0−5.0 −4.0−3.0−2.0−1.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 −1.0 −1.0 −1.0 −1.0 −2.0 −2.0 −2.0 −2.0 −3.0 −4.0 −3.0 −3.0 −3.0 −5.0 −4.0 −6.0 −4.0 −4.0 −7.03) 4  c) S=  ,4  9   11 a) S=  − ,3  5   5 7 d) S =  x ∈ R | < x <  2 8   2 2b) S=  ,  5 9  e) S = {x ∈ R | x ≥ −2 ou x ≤ −5}
  • 4. 4)a) y = | x | +2 c) y = x2 - 4b) y = | x +2| d) y = |x 2 – 4|5)a) y = x c) y = x +3b) y = x +3 d) y = 4 x
  • 5. 6)a) F exemplo: (5 + 3) 2 ≠ 5 2 + 3 2 e) F O correto éb) V log 3 (x ⋅ y ) = log 3 x + log3 y, x.y > 0 32 + 42 ≠ 3 + 4 2 1 2 +1c) F exemplo: f) F exemplo: + ≠ 1 2 1+ 2d) F exemplo: (− 2 + 1)2 ≠ −2 + 1 g) V7)a) f(x) = 2x c) h(x) = 2x + 2 e) g(x) = 3.2x Observação: 3.2x ≠ 6x x  1b) g( x) =   x  2 1  d) f(x) =   - 3 x 2 f) h(x) = 28)a) Dom f = {x ∈ R / x > 0} b) Dom f = {x ∈ R / x > 0}
  • 6. c) Dom f = {x ∈ R / x > −1} e) Dom f = {x ∈ R / x < 0 }d) Dom f = {x ∈ R / x > 2} f) Dom f = {x ∈ R / x > 0}9)a) c)b) d)
  • 7. 10) a) f o g( x ) = sen ( x) + 10g o f ( x ) = sen ( x + 10 )f o f (x ) = x + 10 + 10g o g ( x ) = sen( sen ( x))b) f o g( x ) = ( 2 x − 7) 2 + 3( 2 x − 7)g o f ( x ) = 2( x 2 + 3x ) − 7f o f ( x) = ( x 2 + 3x ) 2 + 3( x 2 + 3 x)g o g ( x ) = 2( 2x − 7) − 711) a) 2x-3+h −1b) x ( x + h)c) 2x+4+h