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)?

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

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

C. g(x) = (x - 6)2 + 5
D. g(x) = (x + 5)2 - 6

Answer 1

To translate to the left n units we must add n to x in the original equation...

y=x^2 becomes:

y=(x+6)^2

y=x^2+12x+36

To now shift y down by 5 units we subtract 5 from y

y=x^2+12x+36-5

y=x^2+12x+31 which is equal to:

y=(x+6)^2-5