Describe the end behavior of each function.
A. y=x^4 +5

B. Y=-x^5+5x^3-2x+3

Question

Describe the end behavior of each function.
A. y=x^4 +5

B. Y=-x^5+5x^3-2x+3

misty1212 · Answer

HI!!

misty1212 · Answer

the first one has degree 4, which is even

misty1212 · Answer

also it has a positive leading coefficient (it is 1)

misty1212 · Answer

therefore as $x\to \infty$ you have $x^4+5\to\infty$ and as $x\to -\infty$ you have $y^4+5\to \infty$

misty1212 · Answer

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misty1212 · Answer

do you know what a polynomial of odd degree with negative leading coefficient looks like?

anonymous · Answer

No, sorry

misty1212 · Answer

ok lets start with a polynomial of degree 1, a  line, with negative leading coefficient, like say $y=-x+1$ you know what that looks like?

anonymous · Answer

Yes

misty1212 · Answer

it has the same "end behavior' as any polynomial of odd degree with negative leading coefficient

anonymous · Answer

Ok

misty1212 · Answer

you got that? goes to positive infinity as x goes to negative infinity, and negative infinity as x goes to positive infinity

anonymous · Answer

So the answer is x^4+5 > infinity

anonymous · Answer

?

misty1212 · Answer

do you know what "end behavior" means?

anonymous · Answer

Yeah

anonymous · Answer

Refer to the attachment

anonymous · Answer

both a and b  are functions that have an odd number as their highest exponential degree. so the as x gets bigger, so does y. and as x gets smaller, so does y. the answer for the limit for both is 
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