Paridade de função Apresentação

5 Slides • 2 Questions

1

Paridade de função

Par ou Ímpar?

2

Função par

Sejam $A$ um subconjunto de $\mathbb{R}$ e $f:A\rightarrow\mathbb{R}$ uma função.

Define-se:

f\left(x\right)\

é par se, e somente se:

f\left(x\right)=f\left(-x\right),\forall x\in A

3

Exemplo:

Seja $f:\mathbb{R}\rightarrow\mathbb{R}$ , definida por: $f\left(x\right)=x^2$

Temos: $f\left(-x\right)=\left(-x\right)^2=x^2$

Logo: $f\left(x\right)=f\left(-x\right)$

Portanto, $f\left(x\right)$ é par.

4

Função ímpar

Sejam $A$ um subconjunto de $\mathbb{R}$ e $f:A\rightarrow\mathbb{R}$ uma função.

Define-se:

f\left(x\right)\

é ímpar se, e somente se:

f\left(-x\right)=-f\left(x\right),\forall x\in A

5

Exemplo:

Seja $f:\mathbb{R}\rightarrow\mathbb{R}$ , definida por: $f\left(x\right)=x^3$

Temos: $f\left(-x\right)=\left(-x\right)^3=-x^3$

-f\left(x\right)=-x^3

Logo: $f\left(-x\right)=-f\left(x\right)$

Portanto, $f\left(x\right)$ é ímpar.

6

Multiple Select

Recordando... vimos que a função $f\left(x\right)=x^{2\ }$ é

1

Par

2

Ímpar

7

Multiple Select

E a função $f\left(x\right)=x^{3\ }$ é

1

Par

2

Ímpar

Paridade de função

Par ou Ímpar?

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