Step-by-step explanation:
you do know that f(x) is the same as y ?
because the y value is the result of a function (in 2-dimensional space).
for such questions we only need to look at the term with the highest exponent of x.
with large values of x this term then "drowns" out all other terms regarding the dimension of the "limit" the range (= functional results) of the function can reach.
so, the term with the highest exponent of x is here
-4x⁶
all the other terms with x⁵, x⁴, x³, ... are much, much smaller in absolute value than |-4x⁶| for really large values of x (x going to infinity, but also to -infinity).
as explained, the term -4x⁶ is therefore driving the limit or end behavior of the function.
so, what happens here, when x goes to +infinity ?
then x⁶ goes to +infinity.
and that means 4x⁶ goes to +infinity.
but that means -4x⁶ goes to -infinity !
and when x goes to -infinity ?
then x⁶ still goes to +infinity (remember, multiplying 2 negative values gives a positive result, so any form of squaring incl. any even exponents will already have positive results).
and that means 4x⁶ goes to +infinity.
but again, -4x⁶ goes then to -infinity.
so the right answer choice is the second one, where y goes to -infinity in both cases.
