The function f(x) = x2 – 6x + 9 is shifted 5 units to the right to create g(x). what is g(x)? 3

a. g(x) = (x + 5)2 – 6(x + 5) + 9

b. g(x) = (x2 – 6x + 9) – 5

c. g(x) = (x2 – 6x + 9) + 5

d. g(x) = (x – 5)2 – 6(x – 5) + 9

D.

Step-by-step explanation:

The resulting function after shifting a function f(x),

a unit right = f(x-a),

a unit left = f(x+a),

Here, the given function,

Thus, by the above statement,

After shifting f(x) by 5 unit right, the transformed function,

 ( From equation (1) )

Hence, option 'D' is correct.

f(x) has value 150 at x= 0

and 0 at x= 3

so d(f(x))/dt = slope = -150/3 = -50