#Why is this c?
green steepleBOT
tawdry leaf
because there will be some value between -inf and inf, where the denominator become 0
and at that point, the function breaks
so, its not continuous at that point
gentle pilot
how so?
can u give me an example?
but i do understand what u mean, i just need a clarification
tawdry leaf
see, polynomials, in most cases have a root. no?
the denominator in option C is a polynomial
of degree 4
gentle pilot
do you mean like even root thing
tawdry leaf
do you mean like even root thing
root meaning, points where the expression is 0
gentle pilot
so - inf ^ 4 would be -inf x -inf x -inf x -inf, wouldn't that be positive?
if the polynomial is even, wouldn't negative inf or positive inf have the same positive inf outcome, therefore when dividing, it would be continuous no?
i agree my logic is flawed somewhere, just trying to pinpoint where..
tawdry leaf
so - inf ^ 4 would be -inf x -inf x -inf x -inf, wouldn't that be positive?
see, at x = inf or x = -inf, the whole expression would be close to 0. value exists.
im talking about the values of x, where the denominator itself is 0, not the whole function
gentle pilot
hmm so it would not be continuous since the even polynomial would result in a positive number outcome, therefore wouldn't be continuous for negative intervals? or am i going far off
tawdry leaf
alr
this is wut the denominator's graph would look like
you see that there are 2 values of x where the expression is 0?
gentle pilot
yeah
tawdry leaf
at those points, h(x) would become 1/0
which is undefined
and the graph breaks there
so, it is not continuous at that point
gentle pilot
ohhh i kind of see what you mean
i understand from a graphical dimension , but how would you figure it out with just the function itself?
im guessing it would be applicable for every polynomial?
(if it is below 0)
tawdry leaf
yeah, so look, you just need to know one thing. for a continuous graph, the func should be defined at all points. (this is true if it is a polynomial function)
so, if there is any point where you see that the func is not defined, the graph wont be continuous
tawdry leaf
im guessing it would be applicable for every polynomial?
not really every polynomial. take a quad polynomial, p(x) for example.
there are cases when no real roots exist. so, the polynomial would never be 0 for any x.
in that case 1/p(x) would always be defined and is continuous
so, your job in these cases, where a polynomial is in den.
is to see if any roots to that polynomial exist or no
if it does, graph is not continuous
else it is
gentle pilot
ok thanks
last question, Does the answer mean from the range -5 to 0, and both has to meet the condition of,
x<=-1 and -1 < x <= 0?
tawdry leaf
yeah. so you just need to see if the limits at the breaking points are same or no
if they are, it'll be continuous
or else no
gentle pilot
ok gotchu