please help me and explain in detail , please make sure of the answers

for q 5 its says to a new function

Multiple Choice & Numerical Response - Record on the front cover of exam booklet, ( mark I. When the function y = x3 + x is reflected in the yaxis, the resultant equation is Cy=p-x Dy= -43-x 2. If y is replaced with in the equation y = / (x). then the graph of y = f(x) will be stretched A.) vertically about the x-axis by a factor of 3 B. vertically about the r-axis by a factor of y C. vertically about the r-axis by a factor of D. vertically about the y axis by a factor of Use the following information to answer the next question. The graphs of a function. y = f(x), and its translated image, y = g(x), are shown below. The equation for g(x) could be g (x) =f(x+2)+3 B. g(x) = f(x+3)+2 g(x) =f(x-2)+3 D. g(x) = f(x-3) +24. The graph of the function y = f(x) passes through the point (4, 7), Under a transformation. the point (4 , 7) is transformed to (6, 6). A possible equation for the transformed function is )y - 1 = f(x + 2) B. y - 2 = f(x + 1) C. y + 1 =/(x - 2) D. y + 2 = f(x - 1) Numerical Response #1 The graph of y = f(x) is stretched vertically by a factor of 2 about the x-axis, stretched horizontally by a factor of 4 about the y-axis, and translated 3 units to the right. These transformations can be described by the mapping notation (x, y) - (ax + b, cy + d). The values of a, b, c, and d, respectively, are 432 Numerical Response #2 4+3 The graph of y = f(x). where f(x) = (x -3)2 - 3. is reflected in the y- axis. This produced the same results as would translating the graph of y = f(x), to the left 6 units. 5. The domain of a function f(x) is {x|x 2 -12, x E R} . If function fis transformed to a ne function y - 2 = f[4(x - 2)], then the domain of the new function is A. {x/x 2 5, x ER] B. {x x 2 -1, x ER} C. { x/ x 2 - 46, x ER} D. {x/x 2 -40, x ER}8. For which of the following graphs of y = f(x) would it be true that -f(x) = f(-x) ? C. D. Numerical Response #4 The function y = f(x) is transformed to become the function g(x) = f[b(x)] + 1. The point (12, 40) on the graph of y = f(x) corresponds to the point (6, 41) on the graph of y = g(x). The value of b, to the nearest whole number, is _Use the following information to answer the next question The graph of function f is shown below. Function fis transformed to create function g 6. If g(x) - 8 =fle(x)], then the image point A' will be in which quadrant? Quadrant 1 B. ) Quadrant 2 C. Quadrant 3 D. Quadrant 4 7. The function f(x) = x? + 1 was transformed into g(x) = 4x2 + 1. The single transformation that has been applied is a A. vertical stretch about the x-axis by a factor of 4. B. vertical stretch about the x-axis by a factor of - C. horizontal stretch about the y- axis by a factor of -. D. horizontal stretch about the y- axis by a factor of 2 Numerical Response #3 A vertical stretch factor of & is applied to the graph of y = (x - 3)3 so that is passes through the point 6,3). The value of k, to the nearest hundredth, ismarks. Written Response - Algebraic solutions required, Solutions without adequate support may not receive 1. The function f(x) = lal has been transformed into the function g (x) = -312x- 121 + 5 Complete the following statement. (3 marks) -3(21 x - 61+5 ) "The function f(x) has been trem formed to the function g(x) by stretching horizontally about the 1-axis by a factor of _2 . stretching vertically about the x-axis by a factor of 3 , reflecting in the -G85 , translating units up and units horizontally to the fight" 2.5/ 3 2. The function y = f(x) is shown on the grid below. The function g(x) is defined as g(x) = -f(2(x - 1)). State the point mapping notation for the transformations and sketch the graph of g (x) on the same grid. (2 marks) (3/ 6) 3. The graph of y = vx is transformed to the function shown below. Determine the equation of the transformed function. (2 marks) CUse the following to answer the next question. The graph of f(x) - -(x-1) +4 is shown to the below. 9. Which of the following statements about transformations on y = f(x) is FALSE? A. The domain of y= f (x) is (-00, 4] B. The value of f-'(1) = 4. The graph of x = f(y) will have one x-intercept. The graph of y = f"(x) will have 2 invariant points. - Use the following information to answer the next question. A function y = f (x) is shown below. ( -4, 2) * (2,2) (0, 1) (-2, 0) Three students were asked to write the equation for a transformation of y = f (x) with exactly one invariant point. Their response are shown below: Student #1: y = 2f(x) Student #2: y = f(-3x) + 1 Student #3: x = f(y) Numerical Response #5 The student(s) that are correct are numbered If more than one student is correct, record the student numbers in ascending order 3/2