Rational Functions (College Board AP® Precalculus): Exam Questions

The function is given by .

Find all real zeros of .

Find the -coordinate of any holes in the graph of .

Find the equation of any vertical asymptote(s) of the graph of .

The function is given by .

Find all values of , as decimal approximations, for which , or indicate that there are no such values.

The function is given by .

(i) Find all values of , as decimal approximations, for which , or indicate that there are no such values.

(ii) Determine the end behavior of as increases without bound. Express your answer using the mathematical notation of a limit.

The rational function is given by .

Find all real zeros of . Show the work that leads to your answer.

The graph of has a hole at . Determine the -coordinate of the hole. Express your answer using the mathematical notation of a limit.

State the equation of the vertical asymptote of the graph of . Express the unbounded behavior of near this asymptote using a one-sided limit as .

The rational function is given by .

Determine the domain of .

Solve the inequality . Show the work that leads to your answer, including the use of a sign test.

A bus rental company charges a fixed fee of $250 plus an additional $8 per passenger. If passengers ride the bus, the average cost per passenger, in dollars, is given by the rational function

for .

Find , expressed as a decimal approximation. Include units in your answer.

Find and interpret your answer in the context of the problem.

The function is given by

Use polynomial long division to rewrite as a polynomial expression for all . Show the work that leads to your answer.

The graph of has a hole at . Find the -coordinate of the hole. Express your answer using the mathematical notation of a limit.

The function is given by .

(i) Find all values of , as decimal approximations, for which , or indicate that there are no such values.

(ii) Determine the end behavior of as increases without bound. Express your answer using the mathematical notation of a limit.

The rational function is given by .

Use polynomial long division to rewrite in the equivalent form , where and are polynomials and the degree of is less than 2. Show your work.

Determine the equation of the slant asymptote of the graph of . Justify your answer using the result from part (a) and the end behavior of the remainder term as increases without bound.

A rational function is given in two equivalent analytic forms.

Standard form:

Factored form:

Determine the end behavior of as increases without bound. Express your answer using the mathematical notation of a limit.

Identify the -coordinate of any holes in the graph of .

Solve the equation , or indicate that there are no such values. Show the work that leads to your answer.

Let , where , , and are constants.

The graph of has all of the following features:

• a horizontal asymptote at

• a vertical asymptote at

• a hole at

• an -intercept at

Use the horizontal asymptote to find the value of .

Use the vertical asymptote and the hole to find the value of . Show the work that leads to your answer.

Use the -intercept and the hole to find the values of and . Show the work that leads to your answer.