To determine the location of the [tex]\( x \)[/tex]-intercept for the function [tex]\( f(x) = -2x - 6 \)[/tex], we follow these steps:
1. Understand the Concept of the [tex]\( x \)[/tex]-intercept:
The [tex]\( x \)[/tex]-intercept is the point where the graph of the function crosses the [tex]\( x \)[/tex]-axis. At this point, the [tex]\( y \)[/tex]-coordinate is zero. Hence, we need to find the value of [tex]\( x \)[/tex] when [tex]\( f(x) = 0 \)[/tex].
2. Set the Function to Zero:
Set [tex]\( f(x) = 0 \)[/tex] and solve for [tex]\( x \)[/tex]:
[tex]\[
-2x - 6 = 0
\][/tex]
3. Solve the Equation:
- Add 6 to both sides of the equation:
[tex]\[
-2x = 6
\][/tex]
- Divide both sides by -2:
[tex]\[
x = -3
\][/tex]
4. Determine the Coordinates:
The [tex]\( x \)[/tex]-intercept occurs at [tex]\( x = -3 \)[/tex]. Since the [tex]\( y \)[/tex]-coordinate is 0, the coordinates of the [tex]\( x \)[/tex]-intercept are:
[tex]\[
(-3, 0)
\][/tex]
Thus, the location of the [tex]\( x \)[/tex]-intercept is [tex]\((-3, 0)\)[/tex].
The correct choice is:
[tex]\[
(-3, 0)
\][/tex]
