Question

Question 2

20 pts

If the domain of the coordinate transformation f(x, y) = (y + 2,- x - 4) is (1,-4), (3,-2), (0.-1), what is

the range?

O (-5,-2), (-7,0).(-4,1)

O (3.0), (5.-2), (2,-3)

0 (0,3), (-2,5),(-3,2)

O (-2,-5), (0, -7), (1, -4)

Answer 1

D. (-2,-5), (0, -7), (1, -4)

Explanation:

From Function Theory we must remember that range of a function is the set of images related to elements of the domain. In this case, we must find the image of each of the three elements that forms the domain of
`f(x, y) = (y+2, -x-4)`, which are:
`A(x,y) = (1, -4)`,
`B(x,y) = (3,-2)` and
`C(x,y) = (0,-1)`.

Then we proceed to find all elements of range:

`A(x,y) = (1, -4)`

`f(1,-4) = (-4+2,-1-4)`

`f(1,-4) = (-2,-5)`

`B(x,y) = (3,-2)`

`f(3,-2) = (-2+2,-3-4)`

`f(3,-2) = (0,-7)`

`C(x,y) = (0,-1)`

`f(0,-1) = (-1+2,0-4)`

`f(0,-1) = (1,-4)`

Which corresponds to option D.