First of all, ALL functions are relations, but not all relations are functions.
To answer the question of whether or not this relation is a function, you want to know if any x value goes to more than one y value.
In this case it is easy. Look at what happens when x=0. At x = 0, your equation becomes y^2=4. Both y=2 and y=-2 satisfy that equation. So x=0 goes to two different y values.
It is a relation, but NOT a function.
No, it is not.
Yes
Yes. Think of y as being a function of x. y = f(x) = x2 + 1
x2 + x2 = 2x2
Implicit: x2 + 2y = 5 Explicit : y = (5 - x2)/2
x = -3y = -14
(the shape is an upside down 'u').
It equals x2 - 34
The quadratic expression x2+6x+8 when factorised equals (x+2)(x+4)
It is a many to one function (APEX)
y = x2 + 14x + 21 a = 1, b = 14 x = -b/2a = -14/2*1 = -7
if x2 + 7 = 37, then x2 = 29 and x = ±√29