Transformation Questions

Questions

• 1. Translate y=(x-1)^2+2 by the vector (3)(-1)
• 2. Stretch y=x^2+cosx-rootx in the x-direction with sf 2
• 3. Stretch y^2cosx-2/y+x=10 in the y direction with sf 3
• 4. Reflect y=arcos(x-2) in the x-axis
• 5. What transformations have taken place for the following
• a). x^3+2x+4 to 3x^3+6x+12
• b). x^2+x+4 to 2x^2+2x+4
• c). 2x^3 to 2(x-1)^3
• d). 2x^2-6x+1 to 2x^2-6x-11
• e). (x-1)(x-4) to (x-2)(x-3)

1-4....

• 1. Translate y=(x-1)^2+2 by the vector (3)(-1) : x->x-3 , y->y+1, so sub these in; y+1=((x-3)-1)^2+2, and rearrange to get: y=(x-4)^2+1
• 2. Stretch y=x^2+cosx-rootx in the x-direction with sf 2 : x->x/2, so sub in; (x/2)^2+cos(x/2)-root(x/2) and simplify for:
• x^2 /4+cos(x/2)-root(2x/2)
• 3. Stretch y^2cosx-2/y+x=10 in the y direction with sf 3 : y->y/3, so sub in; (y/3)^2cosx-2/(y/3)+x=10
• (can be simplied to y^2 /9cosx-2/(y/3)+x=10 if wanted)
• 4. Reflect y=arcos(x-2) in the x-axis : x->-x , so sub in; y=arcos(-2-2) and this is the answer.

5....

• 5. What transformations have taken place for the following
• a). x^3+2x+4 to 3x^3+6x+12 : Everything has been multiplied by 3, which is a stretch in the y-direction sf 3
• b). x^2+x+4 to 2x^2+2x+4 : Everything has been doubled except the +4 , which is a stretch in the x-direction factor 1/2
• c). 2x^3 to 2(x-1)^3 : This has been moved one to the right, so it has been translated by (1)(0)
• d). 2x^2-6x+1 to 2x^2-6x-11 : Everything is the same except the +1 has been moved down 12 to get -11, so it has been translated by (0)(-12)
• e). (x-1)(x-4) to (x-2)(x-3) : Expanding these we get x^2-5x+4 and x^2-5x+6 , so we can see it has been moved up 2, so it has been translated by (0)(2)