To find the [tex]\( y \)[/tex]-intercept of the graph of the function [tex]\( f(x) = (-8)(4)^x - 2 \)[/tex], we need to determine the value of [tex]\( f(x) \)[/tex] when [tex]\( x = 0 \)[/tex]. This is because the [tex]\( y \)[/tex]-intercept occurs where the graph crosses the [tex]\( y \)[/tex]-axis, i.e., the point where [tex]\( x = 0 \)[/tex].
Here's a step-by-step solution:
1. Substitute [tex]\( x = 0 \)[/tex] into the function:
[tex]\[
f(0) = (-8)(4)^0 - 2
\][/tex]
2. Evaluate the expression inside the function:
[tex]\[
(4)^0 = 1
\][/tex]
3. Multiply by the coefficient:
[tex]\[
(-8) \times 1 = -8
\][/tex]
4. Subtract 2:
[tex]\[
-8 - 2 = -10
\][/tex]
So, the [tex]\( y \)[/tex]-intercept of the function is [tex]\((-10)\)[/tex]. In coordinate form, the [tex]\( y \)[/tex]-intercept is [tex]\((0, -10)\)[/tex].
Thus, the correct answer is:
[tex]\[ \text{(D) } (0, -10) \][/tex]
