Question

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

Can you show how you worked it out cause I'm not sure on how to plug it in exactly

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.