AP®︎ Precalculus: Topic 1.11 Practice Test

Essential Knowledge: 1.11.A.1

Because the factored form of a polynomial or rational function readily provides information about real zeros, it can reveal information about $x$-intercepts, asymptotes, holes, domain, and range.

Essential Knowledge: 1.11.A.2

The standard form of a polynomial or rational function can reveal information about end behaviors of the function.

Essential Knowledge: 1.11.A.3

The information extracted from different analytic representations of the same polynomial or rational function can be used to answer questions in context.

Essential Knowledge: 1.11.B.1

Polynomial long division is an algebraic process similar to numerical long division involving a quotient and remainder. If the polynomial $f$ is divided by the polynomial $g$, then $f$ can be rewritten as $f(x)=g(x)q(x)+r(x)$, where $q$ is the quotient, $r$ is the remainder, and the degree of $r$ is less than the degree of $g$.

Essential Knowledge: 1.11.B.2

The result of polynomial long division is helpful in finding equations of slant asymptotes for graphs of rational functions.

Essential Knowledge: 1.11.C.1

The binomial theorem utilizes the entries in a single row of Pascal’s Triangle to more easily expand expressions of the form $(a+b)^n$, including polynomial functions of the form $p(x)=(x+c)^n$, where $c$ is a constant.