If the given term is the dominating term of a polynomial function...

Question

If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a)domain (b)range (c)end behavior (d)number of zeros (e)number of turning points

-9x6

Accepted Answer

A certain polynomial function has the following leading term negative 13 X to the eight. Based on this leading term infer the following features of its graph domain range and behavior number of zeros and number of turning points. So based on our leading term, let's find the domain. First part of main is our possible X values. Now, you know you have negative 13 to the eighth, we don't have any discontinuities that we notice. So our domain should be negative infinity to infinity or our range. You know this, we have a negative in front of our 13. This means our graph should be pointing downwards. This means we are coming from the infinity until we get to zero. We are not shifted up vertically. As far as we know. Now, let's find our end behavior. We notice we have an even degree which nine cases eight and we have a negative leading coefficient. Does he have an even degree? This implies as F of X will approach native affinity, X should also approach negative infinity, negative leading coefficient pointing downwards. So F of X also approaches negative infinity means X will also approach infinity. In other words, we are approaching negative infinity as X approaches infinity and negative infinity. Our number of zeros now is based on our degree, our degree is equals to eight. Now, we don't know the exact number of zeros. We just know that there will be up to eight zeros based on our degree. Finally turning points, our number of turning points will be our degree minus what our degree is eight. So we will have up to seven turning points. We notice our answer which has all of our features corresponds to answer D OK. I hope to help you solve the problem. Thank you for watching. Goodbye.

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If the given term is the dominating term of a polynomial function, what can we conclude about each of the following features of the graph of the function? (a)domain (b)range (c)end behavior (d)number of zeros (e)number of turning points -9x6