SOLUTION: polynomial function is given. S(x) = (3/2)x^6-2x^4 (a) Describe the end behavior of the polynomial function. End behavior: y ->as x → ∞ y →as x &#8594

Algebra ->  Linear-equations -> SOLUTION: polynomial function is given. S(x) = (3/2)x^6-2x^4 (a) Describe the end behavior of the polynomial function. End behavior: y ->as x → ∞ y →as x &#8594      Log On


   

Question 1047500: polynomial function is given.
S(x) = (3/2)x^6-2x^4
(a) Describe the end behavior of the polynomial function.
End behavior:
y ->as x → ∞
y →as x → −∞
(b) Match the polynomial function with one of the following graphs
Found 2 solutions by Boreal, stanbon:
Answer by Boreal(15235) About Me  (Show Source):
You can put this solution on YOUR website!
as x goes to positive infinity, y goes to positive infinity, because x^6 defines the function for large x.
as x goes to minus infinity, (-x)^6 is positive and the function goes to positive infinity.
graph%28300%2C300%2C-20%2C20%2C-20%2C20000%2C%283%2F2%29x%5E6-2x%5E4%29

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
polynomial function is given.
S(x) = (3/2)x^6-2x^4
(a) Describe the end behavior of the polynomial function.
Note: The highest power term determines the end behavior
As x goes to +oo, x^6 goes to +oo; so y goes to +oo
as x goes to -oo, x^6 goes to +oo; so y goes to +oo
End behavior:
y ->+oo as x → ∞
y →+oo as x → −∞
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Cheers,
Stan H.
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