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Is it possible to have a polynomial function with no y-intercepts?...

Question

Is it possible to have a polynomial function with no y-intercepts?

is it possible to have a polynomial function with no y-intercepts?



Answers

Can the graph of a polynomial function have no $y$ -intercept? Can it have no $x$ -intercepts? Explain.

Photograph of a polynomial function have no y intercept. So he can No, you can't. Because F zero must exist, right? So after it is, why intercept on any Annie brought Must cross this lie. It can be here and here, for example. So the phenomenal function must be continuous. But there's no continuity. Right? So if we have a point here and a point here, so they must be continuous. So there have to be a why intercept?

Okay, So is it possible for polynomial function to not have any Y intercepts? Well, the domain of a polynomial is all riel X values. So if the domain doesn't equal X equals zero, then it's not a polynomial, because it's continuous all over the graph. So while you can have it be pleasant First quadrant, 2nd 3rd 4th quadrant the domain is still relevant because it goes beyond what we see on the graph, because eventually this will cross the Y axis, and we have a way intercept. So if it doesn't include X equals zero that it's not a polynomial.

Problem. 86. Can a graph of polynomial function have no axe Intercept? Yes, you can. Off course you can't. So, like why you goes toe x square plus one So he doesn't have intercepts, right? We can claim that if that degrees are it must force to the left and rights to the right or or writers to the left and force the right. So there has to be a here. The access And there has to be a point between this graphs because it's continuous. Right? There has to be one, at least one. So if a paranormal function doesn't have, ah acts intercepts, it has to be even degree, right?

Okay, so is it possible to graph polynomial functions with no intercepts? So let's take, for example, X squared. Now, this is a Perella centered at the origin. Okay, Now, if we add one to it, this moves it up one give or take about here now, What that tells us is we do have a white intercept, but it doesn't come in contact with the X axis whatsoever. So if it's even, it's positive. And so if it's a positive, even integer power, it sometimes won't cross it. Now if you've got it to where it's centered on the X axis, that is not the case, even if it is positive and even But some like this right here, don't ever come in. Contact the X axis, so


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