End Behavior of Polynomials

to find the end behavior (if f(x) is positive or negative infinity) look at ...

just the first term (the number in front and what power X is raised to)

EVEN degree of X, NEGATIVE leading coefficient

x -> -∞, f(x) -> -∞ x -> ∞, f(x) -> -∞ (hint: EVEN means copy the sign of the coefficient which is why y is NEGATIVE here)

ODD degree of X, POSITIVE leading coefficient

x -> -∞, f(x) -> -∞ x -> ∞, f(x) -> ∞ (hint: if its odd degree but positive coefficient, the y signs MATCH the x, so positive is with positive and negative is with negative)

ODD degree of X, NEGATIVE leading coefficient

x -> -∞, f(x) -> ∞ x -> ∞, f(x) -> -∞ (hint: if its odd and negative, the signs are opposite. postive x is negative y and negative x is positive y)

EVEN degree, POSITIVE leading coefficient

x -> -∞, f(x) -> ∞ x -> ∞, f(x) -> ∞ (hint: EVEN means copy the sign of the coefficient which is why y is POSITIVE here)

what stays the same every problem?

x. its is ALWAYS the y you have to memorize: x -> -∞, f(x) -> ??? x -> ∞, f(x) -> ???