Question

Suppose that f(x)=x^2+2 and that g(x) is the result of shifting f(x) down 6 units and left 1 unit. Which of the following is the correct equation for g(x)?

a. g(x)=(x-1)^2-4
b. g(x)=(x-1)^2+4
c. g(x)=(x+1)^2-6
d. g(x)=(x-6)^2+1
e. g(x)=x^2+2
f. g(x)=(x+1)^2-4

please show work!!

Answer 1

To shift a function down 6 units, we subtract 6 from the function. To shift a function left 1 unit, we add 1 to the function.

So, to shift f(x) down 6 units, we have f(x) - 6.
To shift f(x) left 1 unit, we have f(x+1).

Therefore, the equation for g(x) is g(x) = f(x+1) - 6.

Substituting f(x) = x^2 + 2 into the equation, we get:
g(x) = (x+1)^2 + 2 - 6
g(x) = (x+1)^2 - 4

Therefore, the correct equation for g(x) is g(x) = (x+1)^2 - 4.

The answer is f. g(x) = (x+1)^2 - 4.