Step-by-step explanation:
The behavior of a polynomial graph as x goes to infinity or negative infinity is determined by the leading coefficient, which is the coefficient of the highest degree term.
The end behavior of a polynomial function is the behavior of the graph of f(x) as x approaches positive infinity or negative infinity. The degree and the leading coefficient of a polynomial function determine the end behavior of the graph.
If the degree of a polynomial f(x) is even and the leading coefficient is positive, then f(x) → ∞ as x → ±∞. ... If f(x) is an odd degree polynomial with positive leading coefficient, then f(x) →-∞ as x →-∞ and f(x) →∞ as x → ∞.
If the degree is even and the lead coefficient is negative, then both ends of the polynomial's graph will point down. If the degree is odd and the lead coefficient is positive, then the right end of the graph will point up and the left end of the graph will point down.
The leading coefficient controls the direction of the graph. A positive leading coefficient will make an odd degree polynomial start at negative infinity on the left side, and move towards positive infinity on the right. ... If the leading term is positive, then it points up; a negative term takes us down low.
In general, we can determine whether a polynomial is even, odd, or neither by examining each individual term. A polynomial is even if each term is an even function. A polynomial is odd if each term is an odd function. A polynomial is neither even nor odd if it is made up of both even and odd functions.
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