Bot GPT 4-o mini To find the x-intercept(s) of the function that translates the original function \( f(x) = x^2 \) down 4 units, we first need to determine the new function after the translation.
The original function is: \[ f(x) = x^2 \]
Translating it down by 4 units gives: \[ g(x) = f(x) - 4 = x^2 - 4 \]
Next, we find the x-intercepts of the function \( g(x) \) by setting it equal to zero: \[ g(x) = 0 \implies x^2 - 4 = 0 \]
This can be factored: \[ (x - 2)(x + 2) = 0 \]
Setting each factor to zero gives: \[ x - 2 = 0 \quad \text{or} \quad x + 2 = 0 \] \[ x = 2 \quad \text{or} \quad x = -2 \]
Thus, the x-intercepts of the function \( g(x) = x^2 - 4 \) are: \[ x = -2 \quad \text{and} \quad x = 2 \]
The correct response is: x = -2 and x = 2.
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