PRACTICE TEST 2 Find the average rate of change for the function f(x) = -3x2 - x from the values 5 to 6. a. 1/2 b. -2 c. -34 d. -1/6 Solve the inequality algebraically. Express the solution in interval notation. (x - 2)2(x + 9) < 0 a. (-, -9) or (9, ) b. (-, -9] c. (-, -9) d. (-9, ) Find the power function that the graph of f(x) = (x + 4)2 resembles for large values of |x|. a. y = x8 b. y = x2 c. y = x4 d. y = x16 Find the real solutions of the equation 3x3 - x2 + 3x - 1 = 0. a. {-3, 1/3, -1} b. {1/3} c. {1/3, -1} d. {-3, -1/3, -1} Use the Factor Theorem to determine whether x + 5 is a factor of f(x) = 3x3 + 13x2 - 9x + 5. a. Yes b. No Give the equation of the horizontal asymptote, if any, of the function f(x) = (x2 - 5)/(25x x4). a. y = -1 b. no horizontal asymptotes c. y = 0 d. y = -5, y = 5 For the polynomial f(x) = 4(x - 5)(x - 6)3, list each real zero and its multiplicity. Determine whether the graph crosses or touches the x-axis at each x-intercept. a. 5, multiplicity 1, touches x-axis; 6, multiplicity 3 b. -5, multiplicity 1, touches x-axis; -6, multiplicity 3 c. 5, multiplicity 1, crosses x-axis; 6, multiplicity 3, crosses x-axis d. -5, multiplicity 1, crosses x-axis; -6, multiplicity 3, crosses x-axis Solve the inequality algebraically. Express the solution in interval notation. (9x - 5)/(x + 2) 8 a. (-2, 13] b. (-2, 21) c. (-2, 21] d. (-2, 13) Find the intercepts of the function f(x) = x3 + 3x2 - 4x - 12. a. x-intercepts: -2, 2, 3; y-intercept: -12 b. x-intercepts: -3, -2, 2; y-intercept: -12 c. x-intercept: -3; y-intercept: -12 d. x-intercept: -2; y-intercept: -12 Find the x- and y-intercepts of f(x) = (x + 1)(x - 4)(x - 1)2. a. x-intercepts: -1, 1, -4; y-intercept: 4 b. x-intercepts: -1, 1, 4; y-intercept: 4 c. x-intercepts: -1, 1, -4; y-intercept: -4 d. x-intercepts: -1, 1, 4; y-intercept: -4 Form a polynomial f(x) with real coefficients of degree 3 and the zeros 1 + i and -10. a. f(x) = x3 - 10x2 - 18x - 12 b. f(x) = x3 + 8x2 + 20x - 18 c. f(x) = x3 + x2 - 18x + 20 d. f(x) = x3 + 8x2 - 18x + 20 Use the Intermediate Value Theorem to determine whether the polynomial function f(x) = -4x4 - 9x2 + 4; has a zero in the interval [-1, 0]. a. f(-1) = -9 and f(0) = -4; no b. f(-1) = 9 and f(0) = 5; no c. f(-1) = 9 and f(0) = -4; yes d. f(-1) = -9 and f(0) = 4; yes Find the intercepts of the function f(x) = x2(x - 1)(x - 6). a. x-intercepts: 0, -1, -6; y-intercept: 0 b. x-intercepts: 0, 1, 6; y-intercept: 6 c. x-intercepts: 0, 1, 6; y-intercept: 0 d. x-intercepts: 0, -1, -6; y-intercept: 6 Use the graph to find the vertical asymptotes, if any, of the function. a. none b. x = -2 c. y = -2 d. x = -2, x = 0 Find the real solutions of the equation x4 - 8x3 + 16x2 + 8x - 17 = 0. a. {-1, 1} b. {-1, 4} c. {-4, 4} d. {-4, 1} State whether the function f(x) = x(x - 9) is a polynomial function or not. If it is, give its degree. If it is not, tell why not. a. Yes; degree 2 b. No; it is a product c. Yes; degree 0 d. Yes; degree 1 Form a polynomial f(x) with real coefficients of degree 4 and the zeros 2i and -5i. a. f(x) = x4 + 29x2 + 100 b. f(x) = x4 - 2x3 + 29x2 + 100 c. f(x) = x4 + 29x2 - 5x + 100 d. f(x) = x4 - 5x2 + 100 Find the intercepts of the function f(x) = 4x5(x + 3)3. a. x-intercepts: 0, -3; y-intercept: 0 b. x-intercepts: 0, 3; y-intercept: 4 c. x-intercepts: 0, 3; y-intercept: 0 d. x-intercepts: 0, -3; y-intercept: 4 Find the domain of the rational function R(x) = (-3x2)/(x2 + 2x - 15). a. {x|x 5, 3} b. {x|x 5, -3} c. {x|x - 15, 1} d. {x|x -5, 3} The function f(x) = x4 - 5x2 - 36 has the zero -2i. Find the remaining zeros of the function. a. 2i, 6, -6 b. 2i, 3i, -3i c. 2i, 3, -3 d. 2i, 6i, -6i Find a bound on the real zeros of the polynomial function f(x) = x4 - 8x2 - 9. a. -17 and 17 b. -9 and 9 c. -18 and 18 d. -10 and 10