Please help me answering the questions and explain in detail

marks . Written Response- Algebraic solutions required. Solutions without adequate support may not receive Use the following information to answer the next question. The functions f(x) = x + 3 and g(x) = x2- 9 are shown below. 1. Given that j (x) _ 9() "f ( x ) and k(x) = (x) g(x) complete the following. a) Determine the equation and sketch the graph of i(x) = (x) fox) on the grid below. (2 marks) - 6 - 5 -4 - 3 -2 10 12 3 4 56 an AwNI b) Determine the domain and range of k(x). (2 marks) c) Solve the equation (f . g) (x) = 0. (1 mark)Use the following information to answer the next question. The graphs of two functions, f(x) and g (x), are shown below. Two new functions, h(x) and m(x), are defined by A(x) = (f + 9)(x) and m(x) = (g - p)(x). 2. Determine: . The range of m(x) (1 mark) . 4h(-2) + 2m(-3) (1 mark) Use the following information to answer the next question. The graph of a polynomial function is shown below. 3. If the y-intercept of the function is 10, determine the full equation in factored form. (2 marks)J. Lot / (x) be a rational function given by fox) = 4x ham . Where n > 0 and m > 0. The graph has a no horizontal asymptote when B. nam C. Hm d. The domain of the function / (x) = (x-b)(xte) > where b > 0 and c > 0, is A. {xx # b,x# -GxeR] B. {xx =bx* c,xER] C. (x/x # b.x ER] D. (xxER] Use the following information to answer the next question. Four statements about the rational function y= * -b are made below: Statement #1: The function has a vertical asymptote at x = b. Statement #2: The function has a horizontal asymptote at y = 0. Statement #3: The function has an x-intercept at (-b, 0). Statement #4: The function has a point of discontinuity at (b, 2b) Numerical Response #3 The statements above that are false are Numerical Response #4 If f (x) = x2 + x + 5 and g(x) = 2x +4, then (fog )(x) can be expressed in the form ax2 + bx + c, where a, b, c E W. The values of a, b, and c, respectively, areUse the following information to answer the next question . The graphs of y = f(x) and y = g(x) are shown below. 124 -12+ --16+ 5. What graph below is the graph of y = f(x) . g(x) ? A. B. 16 4x 12- 121 18- 8 6 -4 -20 . woked nursite 6 : -124 12- -16+ -16- C. D. 8 - 4- -8 -6 4 21 2 46 -8 6 -4 201 2 46 18+ 8+ -16Use the following information to answer the next question. The graph of h (x) has two unique x- intercepts and is shown below: The characteristics of the graph can be described using the reference numbers as shown in the tables below: Reference Degree Number Reference Leading Reference Range Reference Constant Number Coefficient Number Number Term Even Positive Positive Odd Negative [0, 60 ) Negative (-10,0] Numerical Response #1 Determine the following characteristics. Record answer as a four-digit number in the order shown. Characteristic Degree Leading Range Constant Term Coefficient Reference Number Use the following information to answer the next question. Consecutive integers are integers in a sequence, where the next integer is one greater than the previous integer. For example, expressions that represent consecutive integers can be written as: n, n + 1, n + 2, n + 3, n + 4,... Numerical Response #2 If three consecutive integers have a product of 336, the smallest of the integers isumerical Response - Record on the front cover of exam booklet. -(1 mark each) is 1. A polynomial, f(x) = x* + 4x3 - 3x - 4 is divided by x + 1. The correct statement below A x4 +4x2 - 3x - 4 = (x + 1)(x2 + 5x +2)-2 B.. x4 + 4x2 - 3x -4 = (x+1)(x2+3x -6)+2 C. x4+ 4x2 - 3x -4 = (x+1)(x3 + x2+5x+2)-2 D. x4 + 4x2 - 3x -4 = (x+1)(x3 -x2 +5x - 8)+4 2. Which of the following graphs of polynomial functions corresponds to a polynomial equation with an equation in the form y = a(x - 5)2 (x - 1)3 ? A. B. 203 260 100 -19 D. 200 - 200 100 100 100 -200+