Answer:
C
Step-by-step explanation:
Given f(x) then f(x + h) represents a horizontal translation of f(x)
• If h > 0 then a shift to the left of h units
• If h < 0 then a shift to the right of h units
Here the shift is 5 units right, thus g(x) = (x - 5)²
Given f(x) then f(x) + c represents a vertical translation of f(x)
• If c > 0 then a shift up of c units
• If c < 0 then a shift down of c units
Here the shift is 3 units down, thus g(x) = f(x) - 3
Hence
g(x) = (x - 5)² - 3 → C
