answer the correct choice

Solve the inequality. x2 - 9x 2 0 (-00, 0] or [9, co) O (-0o, - 9] or [0, co) O [-9, 0] O [o, 9]Find the domain of the rational function. h(x) = x+3 x2+ 16 Ofx/x # 0, x #-16} O (x/x # -4, x # 4} C all real numbers Ofx/ x # -4, x # 4, x # - 3}List the potential rational zeros of the polynomial function. Do not find the zeros. f(x) = x5 - 5x2 + 3x +3 O+1, 13 * 3, + +1, + W / H + 3Find the vertical asymptotes of the rational function. f(x) = 3x x - 8 Ox = - 8 Onone X = 3 X = 8Use synthetic division to find the quotient and the remainder. 6x5 - 5x4 + x - 4 is divided by x +g 6x4 2x3 x2 + ix + 3'; remainder E 7 4 S - . :7 0 6x4 - 2x3 + x2 - x + L1; remainder - '? 0 6x4 - 8x3 + 4x2 - 2x + 2; remainder -5 0 6x4 - 8x3 + 5; remainder - Q Find the quotient and the remainder. x4 + 4x2 + 7 divided by x2 + 1 O x2 + 3x + 2; remainder 4 O x2 + 3; remainder 4 O x2 + 3; remainder 0 O x2 + 3x + f:; remainder 0 Give the equation of the horizontal asymptote, if any, of the function. h(x) = 6x3 - 2x - 5 4x + 5 Oy= N/W Oy = 0 Oy = 6 O no horizontal asymptoteUse the Rational Zeros Theorem to find all the real zeros of the polynomial function. Use the zeros to factor f over the real numbers. f(x) = 5x4 - 8x3 + 13x2 - 16x + 6 5 O -2, -1, 1, - 3; f(x) = (x - 1)(5x + 3)(x + 1)(x + 2) Q 1, g; f(x) = (x - 1)(5x - 3)(x2 + 2) 1 Q 2, g; f(x) = (x - 2)(5x - 3)(x2 + 1) O -2, -1, 1, f3; f(x) = (x - 1)(5x - 3)(x + 1)(x + 2) .1 Graph each polynomial function by following Steps 1 through 5. Step 1 : Determine the end behavior of the graph of the function. Step 2 : Find the x- and y-intercepts of the graph of the function. Step 3 : Determine the real zeros of the function and their multiplicity. Use this information to determine whether the graph crosses or touches the x-axis at each x-intercept. Step 4 : Determine the maximum number of turning points on the graph of the function. Step 5 : Use the information in Steps 1 through 4 to draw a complete graph of the function. To help establish the y-axis scale, find additional points on the graph on each side of any x- intercept. f ( x) = (x+ 3)2(2 - x) Step 1: Degree is 3. The function resembles y = -x3 for large values of kxl. Step 2: y-intercept: f(0) = 9, x-intercepts: -3, 1 Step 3: Real zeros -3 with multiplicity two, 1 with multiplicity one. The graph touches the x-axis at x = -3 and crosses the x-axis at x = 1. Step 4: 3 - 1 = 2 Step 5: f(-4) = 5, f(-2) = 3, f(3) = -72 y 16 12+ 4+ -3 2 3 4 8 -4- -8+ -12+ -16+Step 1: Degree is 3. The function resembles y = -x' for large values of kxl. Step 2: y-intercept: f(0) = -18, x-intercepts: -3, 2 Step 3: Real zeros -3 with multiplicity two, 2 with multiplicity one. The graph touches the x-axis at x = -3 and crosses the x-axis at x = 2. Step 4: 3 - 1 = 2 Step 5: f(-4) = -6, f(-2) = -4, f(3) = 36 16 y 12+ 8+ 4- 1 3 4 x -4- -8 12+ -16+Step 1: Degree is 3. The function resembles y = -x for large values of Ixl. Step 2: y-intercept: f(0) = 18, X-in Main Content -3, 2 Step 3: Real zeros -3 with multiplicity two, 2 with multiplicity one. The graph touches the x-axis at x = -3 and crosses the x-axis at x = 2. Step 4: 3 - 1 = 2 Step 5: f(-4) = 6, f(-2) = 4, f(3) = -36 12 8 4+ 4-3 -2 -1 1 3 3 4 -8+ -12+ -16O Step 1: Degree is 3. The function resembles y = -x for large values of kxl. Step 2: y-intercept: f(0) = -9, x-intercepts: -3, 1 Step 3: Real zeros -3 with multiplicity two, 1 with multiplicity one. The graph touches the x-axis at x = -3 and crosses the x-axis at x = 1. Step 4: 3 - 1 = 2 Step 5: f(-4) = -5, f(-2) = -3, f(3) = 72 y 16 12+ 4- -1 1 2 3 4 -8 -12+ -16Find the quotient and the remainder. 8x2 + 30x - 8 divided by x + 4 0 8x + 2; remainder 0 0 8x - 2; remainder 4 0 8x - 2; remainder O O x - 2; remainder 0