Question

Which transformation have been placed on the function f(x) = [x] to create g(x) = 1/2 [x-3] - 4

Answer 1

The 3 transformations applied are:

• A horizontal translation of 3 units to the right

,

• A vertical compression by a factor of 2

,

• A vertical translation of 4 units down

Step-by-step explanation

To create function g(x), three transformations were applied. Note that g(x) is,

`g(x)=(1)/(2)f(x-3)-4`

The constant 3 was subtracted from the variable, which represents a horizontal translation of 3 units to the right. Also, the function was multiplied by 1/2, which represents a vertical compression by a factor of 2, and, finally, we subtract 4 from the function, which is a vertical translation of 4 units down.