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These things will look like their first term in the end
i.e. it will have the same long behavior as \(f(x) = - 4x^4\)which will have the same end behavior as \(f(x) = -x^2\) \(\longleftarrow\) Do you know what that looks like?
yes like this?|dw:1442450350337:dw|
End Behavior of a Graph of a Polynomial Function:
If it has an odd degree, the ends will end in opposite direction. If it has a positive lead coefficient then on the left the graph will be down and go up on the right. If it has a negative lead coefficient then it starts up on the left and down on the right.
If it has an even degree, the ends will end in the same direction. If it has a positive lead coefficient, both will go up. If it has a negative lead coefficient they both will end downwards.
Does it make sense?
So, in your equation: P(x)= -4x^4-3x^3+x^2+4. The degree, which is four, is even. So both ends will end in the same direction. The leading coefficient, -4, is negative so both ends will go downward.
You did it correctly, but it's always best to know how to determine the end behavior in general for future questions.
oh okay so you just draw the end behavior or do you have to explain it with x is approaching etc.
Well, if they're asking you to explain the end behavior it's simply that both ends will go downwards. If they ask you to explain, just tell them how the degree (4) is even, etcetc.
oh ok thx
Correct, and if you had something like \(-7x^5\) as the leading term, then you compare it to \(-x\)