If f(x) = x^2 and g(x) = 1/2 f(x + 3) + 6 Describe the transformation(s)​

First, let's define some transformations:

Horizontal translation:

For a function f(x) a horizontal translation of N is written as

g(x) = f(x - N)

If N is positive we have a translation to the right

if N is negative we have a translation to the left.

Vertical translation:

For a function f(x) a vertical translation of N is written as

g(x) = f(x) + N

If N is positive we have a translation up

if N is negative we have a translation down

Vertical dilation.

For a function f(x), a vertical dilation of scale factor k is written as:

g(x) = k*f(x)

Now we can see that in our problem we have:

g(x) = (1/2)*f(x + 3) + 6

Then if we start wit f(x) we have:

first we have a dilation of scale factor k = 1/2

g(x) = (1/2)*f(x)

then we have a translation of 6 units up

g(x) = (1/2)*f(x) + 6

then a translation of 3 units to the left

g(x) = (1/2)*f(x - 3) + 6

answer 1 : option "c"

answer 2 : option "d"

answer 3 : option "b"

answer 4 : option "d"

answer 5 : option "b"

answer 6 : option "a"

answer 7 : option "c"

answer 8 : option "d"

answer 9 : option "c"

answer 10 : option "d"

answer 11 : option "c"

answer 12 option "b"

answer 13 option "c"

answer 14 option "c"

answer 15 option "d"

answer 16 option "a"

answer 17 option "b"

answer 18 option "c"

answer 19 option "a"

answer 20 option "a"

answer 21 option "c"

d