PROGRAMA DE PÓS GRADUAÇÃO EM ENSINO DE CIÊNCIAS EXATAS – PPGECE

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Ficha catalográfica elaborada pelo DePT da Biblioteca Comunitária da UFSCar

S586fa

Silva, Roberta Angela da.

Folhas de atividades para o ensino de função afim e quadrática : conceito e aplicações / Roberta Angela da Silva. -- São Carlos : UFSCar, 2015.

164 f.

Dissertação (Mestrado) -- Universidade Federal de São Carlos, 2014.

1. Matemática - estudo e ensino. 2. Conceitos. 3.

Estudantes - atividades. 4. Funções. 5. Autonomia. I. Título.

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A tabela de Juninho associa a área pintada com o preço a ser pago. São duas grandezas relacionadas por uma regra estabelecida pelo pintor. Você se lembra de que chamamos isso de função?

Juninho procurou a palavra FUNÇÃO em um dicionário, e viu que ela tem os seguintes significados:

a) Festa; festividade.

b) Trabalho realizado por um determinado órgão dos seres vivos. c) O que é atribuído a uma pessoa em uma equipe de trabalho.

d) Dependência de uma quantidade, determinada pelo valor de outra principal. e) Dança, fandango.

3) Qual desses itens é o significado usado na Matemática? Resposta: _____________

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5 = 35, 10 = 45, 15 = 55... Sendo assim, responda: 17 = _____________

5) Se a área pintada for , quanto deverá ser pago?

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Na figura abaixo o gráfico é a linha mais grossa em cor vermelha. Estamos interessados em examinar a variação da função em intervalos iguais de m². Ou seja, o quanto varia o preço em relação à área pintada. Veja e depois preencha a tabela ao lado:

O que você notou?

____________________________________________

Intervalo em m²

Variação de Valor

(R$)

0 a 5 5 − 0 = 35 − 25 = 10

5 a 10

10 a 15

15 a 20

20 a 25

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Consideremos outro exemplo, sendo agora em intervalos de 1m². Veja o gráfico e depois preencha a tabela ao lado:

Intervalo em m²

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(R$)

0 a 1 1 − 0 = 27 − 25 = 2

1 a 2

2 a 3

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O que você notou? _____________________________________________ Você conseguiria escrever o que essas tabelas têm em comum?

______________________________________________________________________

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O que você notou?

_____________________________________________________________________________

7) Consideremos outro exemplo de função: 0 2=I +BL$ Quanto você acha que vale sua taxa de variação? Resposta: ______________________

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8) Vamos pensar agora em um exemplo de Física!

Você já aprendeu, na Física, que uma partícula, como um carrinho, em Movimento Retilíneo Uniforme percorre uma trajetória reta com velocidade CONSTANTE.

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TEMPO (s) 0 1 2 3 4 5 6

POSIÇÃO (m) 1 4 7 10 13 16 19

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Marque os pontos da tabela no sistema cartesiano abaixo e desenhe o gráfico da função unindo os pontos em uma reta.

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a) Em que posição o carrinho estará aos 10 segundos? _______________________ b) Em que posição o carrinho estará aos 15 segundos? _______________________ c) Em cada segundo que passa, quanto o carrinho anda? ______________________ d) Se o número de segundos for , como poderemos escrever a posição do carrinho?

e) Quanto é a taxa de variação de espaço (posição) sofrida pelo carrinho a cada segundo? _______________

f) Qual o nome que a física dá para essa variação? ___________________

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Função Afim

Uma função chama-se afim quando existem constantes reais e , com ≠ 0, tais que

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Pergunta:

Qual a taxa de variação da função = + ? Resposta: __________________________________

A principal propriedade que caracteriza as funções afins é que sua taxa de variação é

constante.

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André estuda economia e conseguiu um emprego. A sua primeira tarefa era escolher qual banco era mais vantajoso financeiramente para abrir uma conta corrente para movimentar o dinheiro da empresa. Ele consultou as taxas de dois bancos: Banco ABC e banco XY. O banco ABC cobra uma tarifa de manutenção de conta (TMC) da seguinte forma: uma taxa de R$10,00 mensais e mais uma taxa de R$0,15 por cheque emitido. O banco XY cobra de TMC uma taxa de R$20,00 mensais e mais uma taxa de R$0,10 por cheque emitido. Para decidir entre os dois bancos, André fez algumas contas. Ajude-o nessas contas!

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1) Se ele gastar 20 cheques por mês, quanto ele gastará em taxas no banco ABC? ________. E no banco XY? ______________. 2) Se ele gastar 55 cheques por mês, quanto ele gastará em taxas no banco ABC? _______.

E no banco XY? _____________. 3) Se ele gastar 100 cheques por mês, quanto ele gastará em taxas no banco ABC? _______.

E no banco XY? _____________. 4) Se ele gastar 200 cheques por mês, quanto ele gastará em taxas no banco ABC? ______.

E no banco XY? ____________. 5) Se ele gastar 220 cheques por mês, quanto ele gastará em taxas no banco ABC? ______.

E no banco XY? ____________. 6) Se ele gastar 240 cheques por mês, quanto ele gastará em taxas no banco ABC? _______.

E no banco XY? ____________.

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7) Considerando apenas os valores acima, a partir de qual quantidade de cheques mensais o banco XY se torna mais viável financeiramente? ___________________________

8) Qual expressão representa o gasto com taxas mensais no banco ABC? _______________ E no banco XY? _____________________

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9) Preencha a tabela abaixo:

BANCO ABC

Número de cheques 100 120 140 160 180 200 220 240 TAXA MENSAL

BANCO XY

Número de cheques 100 120 140 160 180 200 220 240 TAXA MENSAL

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10) Marque os pontos das duas tabelas no sistema cartesiano abaixo e desenhe os gráficos das duas funções.

11) Destaque o ponto de encontro entre as duas linhas, verificando mais uma vez a partir de que número de cheques o banco XY é mais vantajoso.

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12) André ficou com preguiça de fazer um gráfico. Utilizando álgebra e as expressões do item 8), como você ajudaria André a justificar qual banco é mais viável?

_________________________________________________________________________

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Função quadrática – Aplicações

1)Preparando um campeonato

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Carlos, estudante do primeiro ano do Ensino Médio de um colégio no interior de São Paulo, pediu para que seu professor de educação física organizasse um campeonato de futebol de salão com times de sua classe. Primeiramente a ideia era que participassem desse campeonato apenas os meninos do primeiro ano, que eram quinze. Uma equipe de futebol de salão é composta por cinco jogadores, portanto formaram-se os times A, B e C. Na primeira fase desse campeonato, cada time jogará com cada um dos outros times exatamente duas vezes. Escreva abaixo os jogos que serão realizados por esses três times:

Resposta: ________________________________________________________________ Quantos jogos foram realizados com esses 3 times? Resposta: _____________________

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