1 of 20 5.0 Points Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x) = 2x4 - 4x2 + 1; between -1 and 0 A. f(-1) = -0; f(0) = 2 B. f(-1) = -1; f(0) = 1 C. f(-1) = -2; f(0) = 0 D. f(-1) = -5; f(0) = -3 Question 2 of 20 5.0 Points Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = x2(x - 1)3(x + 2) A. x = -1, x = 2, x = 3 ; f(x) crosses the x-axis at 2 and 3; f(x) touches the x-axis at -1 B. x = -6, x = 3, x = 2 ; f(x) crosses the x-axis at -6 and 3; f(x) touches the x-axis at 2. C. x = 7, x = 2, x = 0 ; f(x) crosses the x-axis at 7 and 2; f(x) touches the x-axis at 0. D. x = -2, x = 0, x = 1 ; f(x) crosses the x-axis at -2 and 1; f(x) touches the x-axis at 0. Question 3 of 20 5.0 Points Find the coordinates of the vertex for the parabola defined by the given quadratic function. f(x) = 2(x - 3)2 + 1 A. (3, 1) B. (7, 2) C. (6, 5) D. (2, 1) Question 4 of 20 5.0 Points The difference between two numbers is 8. If one number is represented by x, the other number can be expressed as: A. x - 5. B. x + 4. C. x - 8. D. x - x. Question 5 of 20 5.0 Points Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x) = x3 - x - 1; between 1 and 2 A. f(1) = -1; f(2) = 5 B. f(1) = -3; f(2) = 7 C. f(1) = -1; f(2) = 3 D. f(1) = 2; f(2) = 7 Question 6 of 20 5.0 Points Solve the following polynomial inequality. 3x2 + 10x - 8 0 A. [6, 1/3] B. [-4, 2/3] C. [-9, 4/5] D. [8, 2/7] Question 7 of 20 5.0 Points Based on the synthetic division shown, the equation of the slant asymptote of f(x) = (3x2 - 7x + 5)/x - 4 is: A. y = 3x + 5. B. y = 6x + 7. C. y = 2x - 5. D. y = 3x2 + 7. Question 8 of 20 5.0 Points All rational functions can be expressed as f(x) = p(x)/q(x), where p and q are __________ functions and q(x) 0. A. horizontal asymptotes B. polynomial C. vertical asymptotes D. slant asymptotes Question 9 of 20 5.0 Points If f is a polynomial function of degree n, then the graph of f has at most __________ turning points. A. n - 3 B. n - f C. n - 1 D. n + f Question 10 of 20 5.0 Points The perimeter of a rectangle is 80 feet. If the length of the rectangle is represented by x, its width can be expressed as: A. 80 + x. B. 20 - x. C. 40 + 4x. D. 40 - x. Question 11 of 20 5.0 Points Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 2x2, but with the given point as the vertex (5, 3). A. f(x) = (2x - 4) + 4 B. f(x) = 2(2x + 8) + 3 C. f(x) = 2(x - 5)2 + 3 D. f(x) = 2(x + 3)2 + 3 Question 12 of 20 5.0 Points Solve the following polynomial inequality. 9x2 - 6x + 1 < 0 A. (-, -3) B. (-1, ) C. [2, 4) D. Question 13 of 20 5.0 Points Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = x3 + 2x2 - x - 2 A. x = 2, x = 2, x = -1; f(x) touches the x-axis at each. B. x = -2, x = 2, x = -5; f(x) crosses the x-axis at each. C. x = -3, x = -4, x = 1; f(x) touches the x-axis at each. D. x = -2, x = 1, x = -1; f(x) crosses the x-axis at each Question 14 of 20 5.0 Points The graph of f(x) = -x3 __________ to the left and __________ to the right. A. rises; falls B. falls; falls C. falls; rises D. falls; falls Question 15 of 20 5.0 Points Write an equation that expresses each relationship. Then solve the equation for y. x varies jointly as y and z A. x = kz; y = x/k B. x = kyz; y = x/kz C. x = kzy; y = x/z D. x = ky/z; y = x/zk Question 16 of 20 5.0 Points The graph of f(x) = -x2 __________ to the left and __________ to the right. A. falls; rises B. rises; rises C. falls; falls D. rises; rises Question 17 of 20 5.0 Points Find the x-intercepts. State whether the graph crosses the x-axis, or touches the x-axis and turns around, at each intercept. f(x) = -2x4 + 4x3 A. x = 1, x = 0; f(x) touches the x-axis at 1 and 0 B. x = -1, x = 3; f(x) crosses the x-axis at -1 and 3 C. x = 0, x = 2; f(x) crosses the x-axis at 0 and 2 D. x = 4, x = -3; f(x) crosses the x-axis at 4 and -3 Question 18 of 20 5.0 Points Write an equation in standard form of the parabola that has the same shape as the graph of f(x) = 3x2 or g(x) = -3x2, but with the given maximum or minimum. Maximum = 4 at x = -2 A. f(x) = 4(x + 6)2 - 4 B. f(x) = -5(x + 8)2 + 1 C. f(x) = 3(x + 7)2 - 7 D. f(x) = -3(x + 2)2 + 4 Question 19 of 20 5.0 Points 8 times a number subtracted from the squared of that number can be expressed as: A. P(x) = x + 7x. B. P(x) = x2 - 8x. C. P(x) = x - x. D. P(x) = x2+ 10x. Question 20 of 20 5.0 Points Find the domain of the following rational function. g(x) = 3x2/((x - 5)(x + 4)) A. {x x 3, x 4} B. {x x 4, x -4} C. {x x 5, x -4} D. {x x -3, x 4} \f