Respuesta :
The absolute value function is given below as
[tex]f(x)=|x+2|[/tex]Concept: We will have to explain what is meant by an odd function, even function, or neither
Even function: A function is said to be even if it has the equality below
[tex]f(x)=f(-x)[/tex]is true for all x from the domain of definition.
An even function will provide an identical image for opposite values.
Odd function:A function is odd if it has the equality below
[tex]f(x)=-f(-x)[/tex]is true for all x from the domain of definition.
An odd function will provide an opposite image for opposite values.
Neither: A function is neither odd nor even if neither of the above two qualities is true, that is to say:
[tex]\begin{gathered} f(x)\ne f(-x) \\ f(x)\ne-f(-x) \end{gathered}[/tex]Given that
[tex]\begin{gathered} f(x)=|x+2| \\ f(-x)=|-x+2| \\ f(x)\ne f(-x) \end{gathered}[/tex]Also,
[tex]\begin{gathered} f(x)=|x+2| \\ -f(-x)=-|-x+2| \\ f(x)\ne-f(-x) \end{gathered}[/tex]Therefore,
We can conclude that f(x) = |x+2| is NEITHER an even nor a odd function
