Determine the x-intercept(s) of the function that translates the original function f(x)=x2

Question

down 4 units.(1 point)
Responses

x=−16
and x=16
x equals negative 3.464 and x equals 3.464

x=−4
and x=4
x equals negative 4 and x equals 4

x=−2
and x=2
x equals negative 2 and x equals 2

There are no x-intercepts.

Answer 1

To determine the x-intercepts of the function that translates the original function \( f(x) = x^2 \) down 4 units, we first need to write the new function.

The new function after translating \( f(x) \) down 4 units is:

\[ g(x) = f(x) - 4 = x^2 - 4 \]

Next, we find the x-intercepts by setting \( g(x) = 0 \):

\[ x^2 - 4 = 0 \]

Now, we can solve this equation:

\[ x^2 = 4 \]

Taking the square root of both sides gives us:

\[ x = \pm 2 \]

Thus, the x-intercepts are:

\[ x = 2 \quad \text{and} \quad x = -2 \]

So the correct response is:

x equals negative 2 and x equals 2.