To determine the location of the [tex]\( x \)[/tex]-intercept for the function [tex]\( f(x) = -2x - 4 \)[/tex], follow these steps:
1. Identify the point of interest: 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]-value is zero ([tex]\( y = 0 \)[/tex]).
2. Set up the equation: To find the [tex]\( x \)[/tex]-intercept, set the output [tex]\( f(x) \)[/tex] equal to 0 because at the [tex]\( x \)[/tex]-intercept, the value of [tex]\( y \)[/tex] must be zero.
[tex]\[
0 = -2x - 4
\][/tex]
3. Solve for [tex]\( x \)[/tex]:
[tex]\[
-2x - 4 = 0
\][/tex]
Add 4 to both sides of the equation:
[tex]\[
-2x = 4
\][/tex]
Now, divide both sides by -2:
[tex]\[
x = \frac{4}{-2}
\][/tex]
[tex]\[
x = -2
\][/tex]
4. Write the coordinates: The [tex]\( x \)[/tex]-intercept occurs at the point where [tex]\( x = -2 \)[/tex] and [tex]\( y = 0 \)[/tex].
Therefore, the location of the [tex]\( x \)[/tex]-intercept is [tex]\( (-2, 0) \)[/tex].
Thus, the correct answer is:
[tex]\[ (-2,0) \][/tex]
