Help on these question/ This is math. I give full credit to u and stars. Try to make it simple and neat and organized. Hope u have a good day tutors

Initials: 4. The function f (x) =-g(-x) represents a transformation that can best be described as A) a reflection in the line y = x C) a reflection in the x-axis B) a reflection in the x-axis and the y-axis D) a reflection in the y-axis 5. Which choice best describes the combination of transformations that must be applied to the graph of / (x) = x to obtain the graph of g (x) = / (5x-10)? A) a horizontal stretch by a factor of -5 and a horizontal translation of 2 units to the right B) a horizontal stretch by a factor of - and a horizontal translation of 10 units to the right C) a horizontal stretch by a factor of 5 and a horizontal translation of 2 units to the left D) a horizontal stretch by a factor of - and a horizontal translation of 2 units to the right 6. In the following graph, which transformations must be applied to the blue curve to obtain g(x)? A) a reflection in the x-axis a vertical translation of 4 units down, and a horizontal translation of 2 units to the left B) a reflection in the x-axis a vertical translation of 4 units up, and a horizontal translation of 2 units to the left C) a reflection in the x-axis a vertical translation of 2 units down, and a horizontal translation of 4 units to the left D) a reflection in the x-axis, a vertical translation of 2 units down, and a horizontal translation of 4 units to the right 7. When b > 0, the function g (x) = vbx has what relationship to the base function S ( x) = Vx? A) f(x) is stretched vertically by a factor of / B) f(x) is stretched horizontally by a factor of | C) f(x) is stretched horizontally by a factor of ") and reflected in the y-axis D) f(x) is stretched vertically by a factor of " and reflected in the x-axis Page 3 of 12Initials: {3} E. Lise Long Division to solve the following. Then. check your work using synthetic division. P{_t}=x5+o.r:+lix+ by 1-1 T. Factor the [allowing using the Integral Karo Theorem {you can use synlhor: or long division}. PU} = 21':t + it: .~: 6 Page 12 of 12 Initials: (6) 4. In ballistics, the paths of projectiles are studied. It is known that the greater the speed at which an object is fired, the farther it will travel. For a particular spring-loaded cannon, this relationship can be modelled by d= , where dis the distance, in metres, 10 travelled by the projectile and v is the muzzle speed, in metres per second. a) Graph the distance function and state its domain and range. b) Graph the inverse of the distance function and state its domain and range. c) What does the inverse represent? a) (4) 5. Use the Factor Theorem to determine whether or not the following are factors of the polynomial P(x)=x +3x -6x -8 a) x+1 b x-3 Page 11 of 12Initials: Short Answer (26 marks) (4) 1. Create a graph of g (x) = f(x-1) +2 for the base function f (x) = vx, using transformations. Be sure to graph f(x) as well. 10 10 8 6 -4 -2 2 4 6 8 10 (3) 2. Solve the equation 3 2x +4 +9 =12, x2-2, algebraically. (2) 3. Given the function f (x) =3x +7, determine its inverse. Page 10 of 12Initials: Initials: 20. For a polynomial P(x), if p(-6)=0, then which of the following must be a factor of P(x)? A) x +6 C) x +6 B) x2 -6 D) x-6 Matching (9 marks) Match each definition or explanation given below to its corresponding term. A transformation D image point B mapping reflection C inverse of a relation invariant point 1. the point that is the result of a transformation of the original point on the graph 2. a point that is mapped to itself by the function 3. a rule of correspondence established between sets that associates each element of a set with an element in the same or another set 4. a relation that undoes another relation 5. a change made to a figure or graph of a relation that results in a shift or change in shape of the figure or graph Match the correct term with the correct part of the statement: x* -16x +99x -234x+216 = x -24x3 + 291x -2562 + 20712 x+8 x+8 A quotient C divisor remainder D dividend 6. x* -16x3 +99x3 -234x+216 7. x+8 8. x' - 24x3 + 291x-2562 9. 20712 Page 9 of 12Initials: 18. Which graph represents an odd-degree polynomial function with two x- ntercepts? A) C) B) D) 19. Which of the following graphs of polynomial functions corresponds to a cubic polynomial equation with roots 4, 1, and 3? A) C) B) D) Page 8 of 12Initials: 16. Which graph shows the solution to the radical equation v/10-x = x +2? A) B) D) 17. Given the function y = x' , what are the parameters of the transformed function y= (x+3)' -6 and what is the effect of each parameter on the graph of the original function? A) a = ;, vertical stretch about the x-axis by a factor of = h = -3, horizontal translation 3 units left k = -6, vertical translation 6 units down B) a = 2, vertical stretch about the x-axis by a factor of 2 h = -3, horizontal translation 3 units left k = -6, vertical translation 6 units down C) a = 5, vertical stretch about the x-axis by a factor of 5 h = -6, horizontal translation 6 units left k =-3, vertical translation 3 units down D) a = 2, vertical stretch about the x-axis by a factor of 2 h =-3, horizontal translation 3 units right k = -6, vertical translation 6 units right Page 7 of 12Initials: 13. Which equation of a radical function would have the following domain and range? ( x ( x2 -7, xER} : (yly25, yeR) A) y= Vx+5+7 C) y= Vx-5+7 B) y= Vx+7-5 D) 1= Vx+7+5 14. Which graph shows the graphical solution to the radical equation 0 = Vx +8-2? A) C) B) D) 15. If 8x' -3x3 + 7x+8 is divided by x +9 to give a quotient of 8x' -75.x+682 and a remainder of -6130, then which of the following is true? A) (x+9)(8x' -75x+682)=-6130 B) (x+9)(8x2 -75x+682) =6130 C) &' -3x3 + 7x+8=(x+9)(8x* -75x+682)-6130 D) 8x - 3x3 +7x+8=(x+9)(8x3 -75x+682)+6130 Page 6 of 12Initials: 13. Which equation of a radical function would have the following domain and range? ( x ( x2 -7, xER} : (yly25, yeR) A) y= Vx+5+7 C) y= Vx-5+7 B) y= Vx+7-5 D) 1= Vx+7+5 14. Which graph shows the graphical solution to the radical equation 0 = Vx +8-2? A) C) B) D) 15. If 8x' -3x3 + 7x+8 is divided by x +9 to give a quotient of 8x' -75.x+682 and a remainder of -6130, then which of the following is true? A) (x+9)(8x' -75x+682)=-6130 B) (x+9)(8x2 -75x+682) =6130 C) &' -3x3 + 7x+8=(x+9)(8x* -75x+682)-6130 D) 8x - 3x3 +7x+8=(x+9)(8x3 -75x+682)+6130 Page 6 of 12Initials: _10. What are the coordinates of the invariant point(s) when the function y = vx -2 is reflected in the x-axis? A) (0,-2) C) (0.4) B) (4,-2) D) (4,0) 11. What is the solution to the radical equation -2=--(x-2) ? B ) -6 81 22 12. Which of the graphs shown below represents the base function / (x) = vx (in black) and the stretched function g (x) = x (in red)? A) C) B) D) Page 5 of 12Initials: 8. When the graph of y = vx is vertically stretched by a factor of 16, the point (-13,5) will be translated to point: A) (5,-13) C) (16,80) B) (-13,80) D) (80,-13) 9. Which graph represents the inverse of the graph shown? A) C) B) D) Page 4 of 12Initials: Multiple Choice (1 mark each) Write the block capital letter corresponding to the best choice on the blank in front of each question. 1. Compared to the graph of the base function f (x) = x, the graph of the function 8(x) = (x-7) is translated A) 7 units down C) 7 units to the left B) 7 units to the right D) 7 units up 2. Given the graph of f(x) shown below, what are the coordinates of point A if the transformed graph is represented by g (x) = f (x +2)? A) (-1, -4) B) (3,-4) C) (3,-6) D) (-1,-2) 3. What is the equation of the transformed function, g(x), after the transformations are applied to the graph of the base function f(x) = x , shown in blue, to obtain the graph of g(x), shown in red? A) g(x) -6=(x-4) B) 8(x) = (x-6)-4 C) 8(x) = (x-4)-6 D) g(x) -4=(x-6) Page 2 of 12