Polynomial and Rational Functions Review

Front

What determines the end behavior of a polynomial function?

Back

The end behavior of a polynomial function is determined by the degree of the polynomial and the sign of the leading coefficient.

Front

What is a horizontal asymptote?

Back

A horizontal asymptote is a horizontal line that the graph of a function approaches as x approaches positive or negative infinity.

Front

What does Descartes' Rule of Signs help determine?

Back

Descartes' Rule of Signs helps determine the possible number of positive and negative real roots of a polynomial.

Front

How can you find the number of positive real solutions of a polynomial?

Back

You can find the number of positive real solutions by applying Descartes' Rule of Signs to the polynomial.

Front

What is a vertical asymptote?

Back

A vertical asymptote is a vertical line x = a where the function approaches infinity or negative infinity as x approaches a.

Front

What is the leading coefficient of a polynomial?

Back

The leading coefficient is the coefficient of the term with the highest degree in a polynomial.

Front

How does the degree of a polynomial affect its end behavior?

Back

If the degree is even, the ends of the graph will point in the same direction; if odd, they will point in opposite directions.

Front

What is the significance of the sign of the leading coefficient?

Back

If the leading coefficient is positive, the right end of the graph rises; if negative, it falls.

Front

What is the relationship between the degree of a polynomial and the number of roots?

Back

A polynomial of degree n can have at most n real roots.

Front

How do you find the horizontal asymptote of a rational function?

Back

To find the horizontal asymptote, compare the degrees of the numerator and denominator.