Question

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

Answer 1

This is neither because none of these:
$f(-x) = f(x)$
$f(-x) = -f(x)$

I'm going to plug in π/2 to check if the odd and even function definition work for this problem or not. Let's do that:
$f(-x) = f(x)$
$f(- \frac{ \pi }{2} ) = 1 + sin(- \frac{ \pi }{2} ) = 1-1 = 0$
$f(-x) = -f(x)$
$f( \frac{ \pi }{2}) = 1+sin( \frac{ \pi }{2}) = 1+1 = 2$

As we can see, 0 ≠ 2. Hence, the function is neither odd nor even.