Question

Determine algebraically if f(x)=|x+2|is a functioneven, odd, or neither.

Answer 1

The absolute value function is given below as

`f(x)=|x+2|`

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

`f(x)=f(-x)`

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

`f(x)=-f(-x)`

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:

`\begin{gathered} f(x)\\e f(-x) \\ f(x)\\e-f(-x) \end{gathered}`

Given that

`\begin{gathered} f(x)=|x+2| \\ f(-x)=|-x+2| \\ f(x)\\e f(-x) \end{gathered}`

Also,

`\begin{gathered} f(x)=|x+2| \\ -f(-x)=-|-x+2| \\ f(x)\\e-f(-x) \end{gathered}`

Therefore,

We can conclude that f(x) = |x+2| is NEITHER an even nor a odd function