Chapter 3 Review 1 PDF

AP PRECALCULUS Test Booklet Unit 3 Review 1 1. The function is given by. Which of the following statements is true? (A) is equivalent to and has the same end behavior as the graph of. (B) is equivalent...

AP PRECALCULUS Test Booklet Unit 3 Review 1 1. The function is given by. Which of the following statements is true? (A) is equivalent to and has the same end behavior as the graph of. (B) is equivalent to and has the same end behavior as the graph of. (C) is equivalent to and has the same end behavior as the graph of. (D) is equivalent to and has the same end behavior as the graph of. 2. The rational function is given by. The table gives values of for selected values of. Which of the following statements is true? (A) , so. (B) and is undefined at , so the graph of has a hole at. (C) and is undefined at , so the graph of has a hole at. , , and is undefined at , so the graph of has a vertical asymptote (D) at. AP Precalculus Page 1 of 7  Test Booklet Unit 3 Review 1 3. In the -plane, the graph of the rational function has a vertical asymptote at. Which of the following expressions could define ? (A) (B) (C) (D) 4. The binomial theorem can be used to expand the polynomial function , given by. What is the coefficient of the term in the expanded polynomial? (A) (B) (C) (D) 5. The functions and are given by and. Which of the following statements is true about the remainder when is divided by ? (A) The remainder is , so is a factor of. (B) The remainder is , so is a factor of. The remainder is , so is not a factor of , and the graph of has a slant (C) asymptote. The remainder is , so is not a factor of , and the graph of does not have a (D) slant asymptote. 6. For a polynomial function , and. Which of the following must be true about ? (A) The degree of is even, and the leading coefficient is negative. (B) The degree of is even, and the leading coefficient is positive. (C) The degree of is odd, and the leading coefficient is negative. (D) The degree of is odd, and the leading coefficient is positive. 7. The function is given by. Which of the following correctly describes the end behavior of as the input values increase without bound? Page 2 of 7 AP Precalculus  Test Booklet Unit 3 Review 1 (A) (B) (C) (D) 8. The polynomial function is given by. Which of the following statements about the end behavior of is true? The sign of the leading term of is positive, and the degree of the leading term of is even; therefore, (A) and. The sign of the leading term of is negative, and the degree of the leading term of is odd; therefore, (B) and. The sign of the leading term of is positive, and the degree of the leading term of is odd; therefore, (C) and. The sign of the leading term of is negative, and the degree of the leading term of is odd; therefore, (D) and. AP Precalculus Page 3 of 7  Test Booklet Unit 3 Review 1 9. The table gives values of a polynomial function for selected values of. What is the degree of ? (A) (B) (C) (D) Page 4 of 7 AP Precalculus  Test Booklet Unit 3 Review 1 10. The graph of the polynomial function is shown. Which of the following could define ? (A) (B) (C) (D) 11. The leading term of the polynomial function is , where is a real number and is a positive integer. The factors of include , , and. What is the least possible value of ? (A) (B) (C) (D) 12. The rational function is expressed as the quotient of two polynomial functions and by. The function is given by. If the graph of has a slant asymptote of , which of the following describes ? (A) has degree with leading coefficient. (B) has degree with leading coefficient. (C) has degree with leading coefficient. (D) has degree with leading coefficient. AP Precalculus Page 5 of 7  Test Booklet Unit 3 Review 1 13. The function is given by , and the function is given by. Consider the rational function defined by. Which of the following is true about holes in the graph of in the -plane? The graph of has no holes, because all values of where determine the location of vertical (A) asymptotes. The graph of has holes at and , because all values of where determine the (B) location of holes. (C) The graph of has a hole at , because. The graph of has a hole at , because and both have the common factor of and zero (D) with a multiplicity such that. 14. The rational function is given by , where is a positive integer. For which of the following values of will the graph of have a horizontal asymptote at ? (A) (B) (C) (D) 15. Which of the following names a function with a hole in its graph at and provides correct reasoning related to the hole? The graph of has a hole at because the values of get arbitrarily close to for (A) -values sufficiently close to , but the function is undefined at. The graph of has a hole at because the values of increase without bound for (B) -values arbitrarily close to. The graph of has a hole at because the values of are arbitrarily close to for (C) -values sufficiently close to. The graph of has a hole at because the values of and are (D) arbitrarily close to for -values sufficiently close to. 16. The rational function is given by. In the -plane, which of the following is the slope of a slant asymptote of the graph of ? (A) (B) (C) (D) 17. In the -plane, the graph of a rational function has a vertical asymptote at. Which of the following could be an expression for ? Page 6 of 7 AP Precalculus  Test Booklet Unit 3 Review 1 (A) (B) (C) (D) 18. The rational function is given by. For what input values of are the output values of equal to ? (A) only (B) , , and only (C) , , and (D) , , , and 19. The rational function is given by. On what intervals of is ? (A) (B) (C) , , and only (D) and 20. undefined The table gives values for a rational function at selected values of. The polynomial in the numerator and the polynomial in the denominator of the function have no zeros in common. Based on the information given, which of the following conclusions is possible for the graph of in the -plane? (A) The graph of has an -intercept at. (B) The graph of has a hole at. (C) The graph of has a vertical asymptote at. (D) The graph of has a horizontal asymptote at. AP Precalculus Page 7 of 7