Solve the following:

Find the vertical asymptotes of the rational function. Question 2 (1 point) _I: Use 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 Q 1, g; f(x) = (x - 1)(5x - 3)(x2 + 2) O -2, -1, 1, g; f(x) = (x - 1)(5x - 3)(x + 1)(x + 2) Q 2, g; f(x) = (x - 2)(5x - 3)(x2 + 1) O -2, -1, 1, - g; f(x) = (x - 1)(5x + 3)(x + 1)(x + 2) Question 3 (1 point) Listen List the potential rational zeros of the polynomial function. Do not find the zeros. f(x) = x5 - 5x2 + 3x + 3 $3, + - O Main Content +1, + W/ H O+1, +3 Question 4 (1 point) () Listen Find the quotient and the remainder. x4 + 4x2 + 7 divided by x2 + 1 Ox2 + 3; remainder 4 Ox2 + 3x + 3; remainder 0 Ox2 + 3x + 2; remainder 4 x2 + 3; remainder OQuestion 5 (1 point) () Listen Give the equation of the horizontal asymptote, if any, of the function. h(x) = 6x3 - 2x -5 4x + 5 O y = 6 O no horizontal asymptote Oy = 0 Oy= 2 Question 6 (1 point) () Listen Solve the inequality. x2 - 9x 2 0 O (-00, 0] or [9, co) O [-9, 0] O [0, 9] (-0 -91 or [0. co)Use synthetic division to find the quotient and the remainder. 6x5 - 5x4 + x - 4 is divided by x + = 6x4 - 2x3 + x2 - 4x+2; remainder - 6x4 - 8x3 + 4x2 - 2x + 2; remainder -5 6x4 - 8x3 + 5; remainder - 13 ( 6x4 - 2x3 - x2 + 4x + 5; remainder - Question 8 (1 point) () Listen Find the domain of the rational function. h(x) = _x+3 x2+ 16 O all real numbers Ofx/x # 0, x#-16} O (x/ x # - 4, x # 4, x #-3} O (x/x # -4, x # 4}Question 9 (1 point) _Il 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 kx|. 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+ 3 -8+ 12+ Step 1: Degree is 3. The function resembles y = -x3 for large values of kl. 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 16 12-O 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 16 y 12+ -8- -12+ -16+ Step 1: Degree is 3. The function resembles y = -x3 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 164X 12 8- 3Step 1: Degree is 3. The function resembles y = -x' for large values of Ixl. 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 12 -2 . 3 -8+ -12+ -16- 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 12+ 2( ) Step 1: Degree is S. Ine UICLon Testifies y - -x- UI dige values UI pq. 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 + 8- 3 -12+ -16+ Question 10 (1 point) Listen Find the quotient and the remainder. 8x2 + 30x - 8 divided by x + 4 Ox - 2; remainder 0 8x + 2; remainder 0 8x - 2; remainder 4Question 10 (1 point) _I: Find the quotient and the remainder. 8x2 + 30x - 8 divided by x + 4 O x - 2; remainder 0 0 8x + 2; remainder 0 0 8x - 2; remainder 4 0 8x - 2; remainder 0