Please solve all problems and show all work. Please show work/justification on paper if possible. All questions are provided below. Complete questions 1-12.

1. For a polynomial function f, lim f(x) = co and lim f(x) = -co. Which of the following must be true about f ? (A) The degree of f is even, and the leading coefficient is negative. (B) The degree of f is even, and the leading coefficient is positive. (C) The degree of f is odd, and the leading coefficient is negative. (D) The degree of f is odd, and the leading coefficient is positive. 2. For the polynomial function g, lim g(x) = -90. Which of the following expressions could define g(I) ? (A) -5x - 214 3) -5x2 - 217 (0) -9000m - (D) -x3 + 214 3. The function f is given by f() = -2x' + 5x* + 6:2 - 3. Which of the following correctly describes the end behavior of f as the input values increase without bound? (A) lim f(x) = 00 (B) lim f(I) = -00 1+00 (C) lim f(x) = 00 24 - 00 ' (D) lim f(x) = -00 1 1-00 4. The polynomial function p is given by p(x) = -4x" + 3x* + 1. Which of the following statements about the end behavior of p is true? The sign of the leading term of p is positive, and the degree of the leading term of p is even; therefore, (A) lim p(x) = co and lim p(2) = 00. The sign of the leading term of p is negative, and the degree of the leading term of p is odd; therefore, (B) lim p(x) = co and lim p() = -co. 24-00' 2-+00 The sign of the leading term of p is positive, and the degree of the leading term of p is odd; therefore, (C) lim p(x) = -co and lim p(I) = co. The sign of the leading term of p is negative, and the degree of the leading term of p is odd; therefore, (D) lim p(x) = -co and lim p() = co. 1 4-00 5. The function f is given by f(x) = 520 - 2x* - 3. Which of the following describes the end behavior of f ?3.4 Homework lim f(z) = -co and lim f(z) = -00 (A) lim f(x) = co and lim f(x) = 00 (B) 2-+00 lim f(x) = -co and lim f (x) = 00 (C) lim f(z) = co and lim f(1) = -00 (D) 1-00' The rate of people entering a subway car on a particular day is modeled by the function R, where 6. R(t) = 0.03t3 - 0.846t? + 6.587t + 1.428 for 0 2. Which of the following must be true? (A) The graph of g has a minimum at I = 2. (B) The graph of g has a maximum at I = 2. (C) The graph of g has a point of inflection at I = 2, is concave down for a > 2. (D) The graph of g has a point of inflection at I = 2, is concave up for I 2. 9. -1 3 5 7 f(x) -36 4 0 12 f are given in the table, which of the following must be true? Values of the polynomial function f for selected values of I are given in the table. If all of the zeros of the function Page 2 of 4 AP Precalculu3.4 Homework (A) The function f has a local minimum at (-1, -36). (B) The function f has a local minimum at (5, 0). (C) The function f has a local maximum at (3, 4). (D) The function f has a local maximum at (1, 0). 10. 3+ -2 -2 -3- Graph of g The graph of the polynomial function g is shown. The function f is defined for 0