Is the number farthest from zero always the greater number?

No, not always.

Yes in some cases, like 100 is greater than 0. But -100 is less than zero. So it depends on the number.

No it is not, in most common number systems.

Step-by-step explanation:

Negative numbers can be far from 0 in magnitude, however, they are always smaller than 0 itself. The only common number system that has no negative numbers are the Natural numbers, so the Answer should be more precisely "No it is not, with the exception of Natural numbers." My assumption is that the question is posed in context of the most commonly used system of Real numbers and so the answer is negative.

the 4th choice is the correct one

step-by-step explanation:

guess at question:

a vertical line intersects the graph of g(x,y) = 0 at two points. what conclusion follows about the function f(x) implicitly defined by g(x,f(x)) = 0?

the domain of f(x) cannot include the x coordinate of any such vertical line.

informally, f(x) is not a function, and

g(x,y)=0 cannot be solved for y uniquely.

the relation r = {(x,y) such that g(x,y) = 0} is a function if

for all (a,b) ∊ r and (c,d) ∊ r, a=c implies b=d.

step-by-step explanation: