Polynomial functions?

Question

explain how the sign of the coefficient of the leading term (term with the highest degree) can help you decide if the graph points up or points down as the value or x gets greater and greater.

thanks so much!

Answer 1

If the polynomial is of an even degree, like x² or x^4 or x^(12), then if the sign of the leading coefficient is positive then the polynomial tends to positive infinity as x goes to negative or positive infinity.  If the sign of the leading coefficient is negative then the polynomial tends to negative infinity as x goes to negative or positive infinity.

If the polynomial is of an odd degree, like x³ or x^5 or x^(11), then if the sign of the leading coefficient is positive then polynomial tends to positive infinity as x goes to positive infinity and the polynomial tends to negative infinity as x goes to negative infinity.  If the sign of the leading coefficient is negative then the polynomial tends to negative infinity as x goes to positive infinity and the polynomial tends to positive infinity as x goes to negative infinity.

Hope this helps you!