Question 1 40 times a number added to the negative square of that number can be expressed as: A. A(x) = x2 + 20x. B. A(x) = -x + 30x. C. A(x) = -x2 60x. D. A(x) = -x2 + 40x. Question 2 Solve the following polynomial inequality. 9×2 6x + 1 < 0 A. (-?, -3) B. (-1, ?) C. [2, 4) D. Ø Question 3 Find the domain of the following rational function. f(x) = 5x/x - 4 A. {x ?x ? 3} B. {x ?x = 5} C. {x ?x = 2} D. {x ?x ? 4} Question 4 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 5 "Y varies directly as the nth power of x" can be modeled by the equation: A. y = kxn. B. y = kx/n. C. y = kx*n. D. y = knx. Question 6 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 7 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 8 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) = x4 - 9x2 A. x = 0, x = 3, x = -3; f(x) crosses the x-axis at -3 and 3; f(x) touches the x-axis at 0. B. x = 1, x = 2, x = 3; f(x) crosses the x-axis at 2 and 3; f(x) crosses the x-axis at 0. C. x = 0, x = -3, x = 5; f(x) touches the x-axis at -3 and 5; f(x) touches the x-axis at 0. D. x = 1, x = 2, x = -4; f(x) crosses the x-axis at 2 and -4; f(x) touches the x-axis at 0. Question 9 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. Quest
ion 10 The difference between two numbers is 8. If one number is XXXXX by x, the other number can be expressed as: A. x – 5. B. x + 4. C. x – 8. D. x – x. Question 11 Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function. g(x) = x + 3/x(x + 4) A. Vertical asymptotes: x = 4, x = 0; holes at 3x B. Vertical asymptotes: x = -8, x = 0; holes at x + 4 C. Vertical asymptotes: x = -4, x = 0; no holes D. Vertical asymptotes: x = 5, x = 0; holes at x – 3 Question 12 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 + 2×2 – 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 13 Find the domain of the following rational function. f(x) = x + 7/x2 + 49 A. All real numbers 210 C. All real numbers ? 77 D. All real numbers Question 14 Find the vertical asymptotes, if any, and the values of x corresponding to holes, if any, of the graph of the following rational function. f(x) = x/x + 4 A. Vertical asymptote: x = -4; no holes B. Vertical asymptote: x = -4; holes at 3x C. Vertical asymptote: x = -4; holes at 2x D. Vertical asymptote: x = -4; no holes Question 15 5.0 Points Use the Intermediate Value Theorem to show that each polynomial has a real zero between the given integers. f(x) = 2×4 – 4×2 + 1; between -1 and 0 A. f(-1) = -0; f(0) = 2 B. f(-1) = -1; f(0) = 1 Hence, there is one zero between x = -1 and x=1 C. f(-1) = -2; f(0) = 0 D. f(-1) = -5; f(0) = -3 Question 16 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) = -2×4 + 4×3 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