Determine the x-intercept(s) of the function that translates the original function f(x)=x2 down 4 units.(
A) x=−16 and x=16
B) x=−2 and x=2
C) x=−4 and x=4
D) There are no x-intercepts.
To find the x-intercepts of a function, we need to set the value of the function equal to zero and solve for x.
The original function f(x) = x^2.
To translate the function downward by 4 units, we need to replace f(x) with f(x) - 4 = 0.
So x^2 - 4 = 0.
This equation can be factored as (x - 2)(x + 2) = 0.
Setting each factor equal to zero, we find x - 2 = 0 or x + 2 = 0.
Solving for x, we get x = 2 or x = -2.
Therefore, the x-intercepts of the translated function are x = -2 and x = 2.
So the correct answer is B) x = -2 and x = 2.