Determine the x-intercept(s) of the function that translates the original function f(x)=x2 down 4 units.(1 point) Responses
x=−4 and x=4
There are no x-intercepts.
x=−2 and x=2
2 x=−16 and x=16
To find the x-intercepts of a function, we need to set y=0 and solve for x.
The original function f(x) = x^2 has x-intercepts when y = 0. Setting y = 0 in the original function gives us x^2 = 0, which means x = 0.
However, we are looking for the x-intercepts of the function that translates the original function down 4 units. In other words, we need to find the x-intercepts of the function g(x) = f(x) - 4.
Setting y = 0 in the function g(x) = (x^2) - 4 gives us (x^2) - 4 = 0. Adding 4 to both sides of the equation gives us x^2 = 4. Taking the square root of both sides gives us x = ±2.
Therefore, the x-intercepts of the translated function are x = -2 and x = 2.
The correct answer is: x = -2 and x = 2.