Question

Determine whether the degree of the function is even or odd and whether the function itself is even or odd.

Answer 1

Answer:

There are Even, Odd and None of them and this does not depend on the degree but on the relation. An Even function: $f(-x)=f(x)$ And Odd one: $-f(x)=f(-x)$

Step-by-step explanation:

1) Firstly let's remember the definition of Even and Odd function.

An Even function satisfies this relation:

$f(-x)=f(x)$

An Odd function satisfies that:

$-f(x)=f(-x)$

2) Since no function has been given. let's choose some nonlinear functions and test with respect to their degree:

$f(x)=x^{2}-4, g(x)= x^{5}+x^{3}$

$f(x)=x^2 -4\Rightarrow f(-x)=(-x)^{2}-4\Rightarrow f(-x)=x^{2}-4\therefore f(x)=f(-x)$

$g(-x)=-(x^{5}+x^{3})\Rightarrow g(-x)=-x^{5}-x^{3}\Rightarrow g(-x)=-g(x)$

3) Then these functions are respectively even and odd, because they passed on the test for even and odd functions namely, $f(-x)=f(x)$ and $-f(x)=f(x)$ for odd functions.

Since we need to have symmetry to y axis to Even functions, and Symmetry to Odd functions, and moreover, there are cases of not even or odd functions we must test each one case by case.