Question

Using the definition of even and odd functions explain why y= sin x+ 1 is neither even or odd ?

Answer 1

A function is even if, for each x in the domain of f, f (- x) = f (x).
 The even functions have reflective symmetry through the y-axis.
 A function is odd if, for each x in the domain of f, f (- x) = - f (x).
 The odd functions have rotational symmetry of 180º with respect to the origin.

 For y = without x + 1 we have:
 Let's see if it's even: 
 f (-x) = sin (-x) + 1
 f (-x) = -sin (x) + 1
 It is NOT even because it does not meet f (- x) = f (x)
 Let's see if it's odd: 
 f (-x) = sin (-x) + 1
 f (-x) = -sin (x) + 1
 It is NOT odd because it does not comply with f (- x) = - f (x)
 Answer:
 It is not even and it is not odd.