To determine the location of the \( x \)-intercept for the linear function \( f(x) = -4x + 12 \), we need to find the value of \( x \) where the function intersects the \( x \)-axis. This occurs when \( f(x) = 0 \), because on the \( x \)-axis, the \( y \)-coordinate is zero.
Here is the step-by-step process to find the \( x \)-intercept:
1. Start with the given function and set it equal to 0:
[tex]\[
f(x) = -4x + 12
\][/tex]
[tex]\[
0 = -4x + 12
\][/tex]
2. Solve the equation for \( x \):
[tex]\[
0 = -4x + 12
\][/tex]
3. Add \( 4x \) to both sides to isolate the term containing \( x \):
[tex]\[
4x = 12
\][/tex]
4. Divide both sides by 4 to solve for \( x \):
[tex]\[
x = \frac{12}{4}
\][/tex]
[tex]\[
x = 3
\][/tex]
Therefore, the \( x \)-intercept of the function \( f(x) = -4x + 12 \) is at the point \((3, 0)\).
So, the correct choice is:
[tex]\[
(3, 0)
\][/tex]
