The original function is y = f(x). if the function translates 6 units left and 4 units up, which function represents the translation?
a) y = f(x - 6) + 4
b) y = f(x + 6) + 4
c) y = f(x - 6) - 4
d) y = f(x + 4) - 6

B

Step-by-step explanation:

Given y = f(x) then

y = f(x ± a) represents a horizontal translation parallel to the x- axis.

• If + a then a shift of a units left ←

• If - a then a shift of a units right →

Here f(x) is translated 6 units left ⇒ f(x + 6)

Given y = f(x) then

y = f(x) ± c represents a vertical translation parallel to the y- axis.

• If + c then a vertical translation up ↑

• If - c then a vertical translation down ↓

Here f(x) is translated 4 units up ⇒ f(x) + 4

Combining the 2 translations gives

y = f(x + 6) + 4 → B