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Answer:
f ( x ) =
5 x 4 + 2 x 3 − x − 4 5 x 4
Graph of f(x)=5x^4+2x^3-x-4.
f ( x ) = − 2 x 6 − x 5 + 3 x 4 + x 3 − 2 x 6
Graph of f(x)=-2x^6-x^5+3x^4+x^3.
f ( x ) = 3 x 5 − 4 x 4 + 2 x 2 + 1 3 x 5
Graph of f(x)=3x^5-4x^4+2x^2+1.
f ( x) = − 6 x 3 + 7 x 2 + 3 x + 1 − 6 x 3
Graph of f(x)=-6x^3+7x^2+3x+1.
Solution:
As the input values x get very large, the output values
f ( x )
increase without bound. As the input values x get very small, the output values
f ( x )
decrease without bound. We can describe the end behavior symbolically by writing
{ as x → − ∞ , f ( x ) → − ∞ as x → ∞ , f ( x ) → ∞
In words, we could say that as x values approach infinity, the function values approach infinity, and as x values approach negative infinity, the function values approach negative infinity.
We can tell this graph has the shape of an odd degree power function that has not been reflected, so the degree of the polynomial creating this graph must be odd and the leading coefficient must be positive.