please answer all the questions and somone helppppp i have an exam in 3 hrs

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

not all the questions are cropped its only for q 5 its says to a new function , I covered the answers because it's all wrong and nothing is incomplete . please comment if any question doesn't make sense to you

• it's math 30-1 transformation unit

I have the answers for mc and nr but i want a full explanation of steps etc

1. D
2. B
3. B
4. C
5. B
6. B
7. C

Numeric

1. 4320
2. 6
3. 0.11

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}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, isDates Pages Numerical Response # 2 :- solution :- 4 = 1 (10) = (x- 3) - 3 is reflected in the y-aries it will produce the same eresult as translating the graph y= flow to the left 6 unit . Hous iit's come let see if. if you reflect it in the y-aris, you will get y - f (- x ) which will be ( - ( 2 - 3 ) 1 2 - 3 . Now, let calculate the translating distance as mentioned in the question the graph produce same Result 50, f ( x ) = + ( - 1 ) (2-3)2 - 3 3 (-2-3) 2-3 on simplifying it, Take square rest on both side (2-3)2-3 = (-X-3) "-7 J( x - 3)2 = ( - X - 3)2 This equation means that distance from 1=-3 2= 3 is tolal distance 6 to move from - 3 to 3.Payre Numerical Response # 3, solution : 2 Given original function 4 = (x-3). To stretch the it vertically by a factor of K wee will need to modify it ie 4 = K (x -3)3 Now let substitute the point ( 6, 3) into modified equation : 3 = K ( 6 - 3) 3 3 = K (33 ) 3 = K(27) K = Vo Now find the value of K to the nearest hundredth we can comeest 1/9 into decimal : 9 do the wallve of k to the nearest 10oth 0all . Note:. This means you need to stretch vertical by factor of 0-110 approximately