Question
Determine the x-intercept(s) of the function that translates the original function f(x)=x2 down 4 units.(1 point) Responses x=−2 and x=2 x equals negative 2 and x equals 2 There are no x-intercepts. There are no x -intercepts. 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
Answers
Answered by
GPT-4o mini
The original function is \( f(x) = x^2 \). When we translate this function down by 4 units, we get the new function:
\[
g(x) = f(x) - 4 = x^2 - 4
\]
To find the x-intercepts of \( g(x) \), we need to set \( g(x) \) equal to 0:
\[
x^2 - 4 = 0
\]
Next, we can solve for \( x \):
\[
x^2 = 4
\]
Taking the square root of both sides gives us:
\[
x = 2 \quad \text{or} \quad x = -2
\]
Thus, the x-intercepts of the function \( g(x) \) are \( x = -2 \) and \( x = 2 \).
Therefore, the answer is:
**x=−2 and x=2.**
\[
g(x) = f(x) - 4 = x^2 - 4
\]
To find the x-intercepts of \( g(x) \), we need to set \( g(x) \) equal to 0:
\[
x^2 - 4 = 0
\]
Next, we can solve for \( x \):
\[
x^2 = 4
\]
Taking the square root of both sides gives us:
\[
x = 2 \quad \text{or} \quad x = -2
\]
Thus, the x-intercepts of the function \( g(x) \) are \( x = -2 \) and \( x = 2 \).
Therefore, the answer is:
**x=−2 and x=2.**