I need help with the following:

f(x) = x^2 +2x + 5 and let E = {-5,-4,-3,-2,-1,0,1,2,3,4,5}

Define the relation R in E as follows: xRy if f(x) = f(y).

I need to find the equivalence classes of R and I'm completely confused, all the examples we've done in class were a lot more simple so I can't get anything out of my notes.

The second problem I'm pretty much done with:

For the following 2 relations on the set L of all living people I'm supposed to state if it is reflexive, symm, anti-symm, and transitive. Then if its a partial order indicate if the set has a maximum, minimum, maximals and minimals and explain what they mean. I'm just having trouble with the latter part.

the relations are:

xRy if X and Y have the same first name

xRy if x and y have the same major

Really appreciate help from anyone. Thanks