F(x) = x; translation 6 units down followed by a
vertical stretch by a factor
of 5
g(x) = 5x = 6

the transformed function becomes: g(x) = 5 x - 30

Step-by-step explanation:

When the function f(x) = x is shifted down by a factor of 6 we have the following transformation:

f(x) --> x - 6

After this, a vertical stretch by a factor of 5 should affect the full functional expression in the following way:

5 ( x - 6) = 5 x - 30

Therefore the transformed function becomes: g(x) = 5 x - 30

option 3 . (5x + 1) - (-10x + 6)

step-by-step explanation:

option 1 :

(4x + 3) + (-9x + 4)

or 4x+3 -9x + 4

or -5x + 7

option 2

(x - 2) - (6x - 9)

or x-2-6x + 9

or -5x + 7

option 3

(5x+ + 6)

or 5x + 1 + 10x -6

or 15x -5

option 4

-4x+2x+7-3x

-7x + 2x + 7

-5x + 7

hence only option 3 did   not satisfy the given simplify expression.