functions and transformations

[teddy7]

Determine the equation of the function that has the indicated transformation applied to the function
f(x) = 3(x + 1)² - 2. (2 marks each)

1. translated up 2 and moved 2 units to the right.
2. reflected in the x-axis and stretched by a factor of 3.

For a. I wrote f(x)=3(x-1)^2
For b. I wrote f(x)= - ___ (x+1)^2 -2

I'm getting really confused with what that blank should be filled with..

 

[HallsofIvy]

Determine the equation of the function that has the indicated transformation applied to the function
f(x) = 3(x + 1)² - 2. (2 marks each)

1. translated up 2 and moved 2 units to the right.
2. reflected in the x-axis and stretched by a factor of 3.

"translated up 2" means that 2 is added to y. "Moved 2 units to the right" means 2 is subtracted from x:
y= 3(x+ 1- 2)^2- 2+ 2= 3(x- 1)^2

"reflected in the x axis" means x is multiplied by -1. "stretched by a factor of 2" means the function (y value) is multiplied by 2:
y= 2((-1(x)+ 1)^2- 2)= 2(-x+1)^2- 4= 2(x- 1)^2- 4.

For a. I wrote f(x)=3(x-1)^2
For b. I wrote f(x)= - ___ (x+1)^2 -2

I'm getting really confused with what that blank should be filled with..

"Stretched by 2" means 1 becomes 2, 2 becomes 4, 3 becomes 6, etc. so it is multiplied by what?