Funções - Aula 2 (Função do 1º grau)
Autor: Guilherme Miguel Rosa | Publicado: 2012-12-20T05:47:00-02:00





EXERCÍCIOS RESOLVIDOS:

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01 - (UFSC) Sabendo que a função f(x) = mx + n admite 5 como raiz e f(-2) = -63 , o valor de f(16) é:



Resolução:

Admitir 5 como raiz quer dizer que quando y = 0 o valor de x é 5. Além disso, temos outro ponto da função, quando x = -2, y = -63. Assim, substituindo o primeiro ponto:

y = mx + n

0 = 5m + n

n = -5m



Substituindo o segundo ponto:

y = mx + n

-63 = -2m + n

-63 = -2m - 5m

-63 = -7m

m = -63

&nbsp; &nbsp; &nbsp; &nbsp; -7&nbsp;

m = 9




Voltando:

n = -5m

n = -5.9

n = -45




Então a função é f(x) = 9x - 45, calculando f(16):

f (16) = 9.16 - 45

f (16) = 144 - 45

f (16) = 99 




Gabarito: 99

  









02 - (ACAFE) Um táxi começa uma corrida com o taxímetro marcando R$ 4,00. Cada quilômetro rodado custa R$1,50. Se ao final de uma corrida, o passageiro pagou R$ 37,00 , a quantidade de quilômetros percorridos foi:

a)26&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;

b)11&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;

c)33&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;

d)22&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;

e)32


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Resolução: A função será y = 1,5x + 4, onde y (preço a ser pago) está em função de x (número de quilômetros rodados).




y = 1,5x + 4



Se ele pagou R$ 37, esse é o y, assim encontramos o número de quilômetros rodados x: 


37 = 1,5x + 4

37 - 4 = 1,5x

33 = 1,5x

x = 22




Gabarito Letra: D









03 - (ACAFE) As figuras abaixo representam gráficos de funções do tipo y = ax + b




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Considere as afirmações:



I. na figura 1 , temos b = 0;

II. na figura 2 , temos a &lt; 0 e b≠ 0;

III. na figura 3, temos a &gt; 0 e b &lt; 0;

IV. na figura 4, temos a = 0; 

V. as figuras 2 e 3 representam gráficos de funções decrescentes;



As afirmações verdadeiras são:



a) I, II e IV&nbsp;&nbsp; &nbsp;

b)II e III&nbsp;&nbsp;&nbsp;

c)II, IV&nbsp; V&nbsp;&nbsp;&nbsp;

d)I e II&nbsp;&nbsp;&nbsp;&nbsp; &nbsp;

e)II, III, IV e V



Resolução:

Item I

Verdadeiro. O b é ponto onde a reta corta o eixo y.



Item II

Verdadeiro. A função é decrescente, então a&lt;0, e a reta não passa na origem, então b≠ 0.



Item III

Falso. A função é crescente mais corta o eixo y acima do eixo x, então temos b&gt;0.



Item IV

Verdadeiro. Neste caso a função é constante, qualquer valor pra x resulta o mesmo y, que é o valor do coeficiente linear b.



Item V

Falso, na figura II o gráfico é decrescente e na figura III é crescente.



Gabarito Letra: A







04 - (UFSM 2011) Em relação ao gráfico abaixo, considerando 2007 como x = 1, 2008 como x = 2 e assim, sucessivamente, a função afim y = ax + b que melhor expressa a evolução das notas em Matemática do grupo II é





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Resolução:
Temos dois pontos na reta II, é o que precisamos para determinar a função. Um dos pontos é (1, 70) e o outro é (3, 65).

y = ax + b
70 = a + b
70 - a = b

y = ax + b
65 = 3a + b
65 = 3a + 70 - a
65 - 70 = 2a
-5 = 2a
a = -5/2

b = 70 - a
b = 70 - (-5)
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2
b =&nbsp; 140 + 5
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2
b = 145
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; 2

y = -5/2x + 145/2

Gabarito Letra: B



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