Answer:
There are Even, Odd and None of them and this does not depend on the degree but on the relation. An Even function: [tex]f(-x)=f(x)[/tex] And Odd one: [tex]-f(x)=f(-x)[/tex]
Step-by-step explanation:
1) Firstly let's remember the definition of Even and Odd function.
An Even function satisfies this relation:
[tex]f(-x)=f(x)[/tex]
An Odd function satisfies that:
[tex]-f(x)=f(-x)[/tex]
2) Since no function has been given. let's choose some nonlinear functions and test with respect to their degree:
[tex]f(x)=x^{2}-4, g(x)= x^{5}+x^{3}[/tex]
[tex]f(x)=x^2 -4\Rightarrow f(-x)=(-x)^{2}-4\Rightarrow f(-x)=x^{2}-4\therefore f(x)=f(-x)[/tex]
[tex]g(-x)=-(x^{5}+x^{3})\Rightarrow g(-x)=-x^{5}-x^{3}\Rightarrow g(-x)=-g(x)[/tex]
3) Then these functions are respectively even and odd, because they passed on the test for even and odd functions namely, [tex]f(-x)=f(x)[/tex] and [tex]-f(x)=f(x)[/tex] 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.
