Question

The function f(x) = x2. The graph of g(x) is f(x) translated to the left 6 units and down 5 units. What is the function rule for g(x)?

Question 18 options:

g(x) = (x + 6)2 - 5

g(x) = (x - 5)2 + 6

g(x) = (x + 5)2 - 6

g(x) = (x - 6)2 + 5

Answer 1

g(x) = (x + 6)^2 - 5

Explanation:

To translate f(x) to the left by 6 units, replace x with x+6.

To translate f(x) down 5 units, replace f(x) with f(x)-5.

Together, these replacements give you ...

... g(x) = f(x+6) -5

... g(x) = (x +6)^2 -5