To find the [tex]\( y \)[/tex]-intercept of the function [tex]\( g(x) = (x-6)(x-3)(x+2) \)[/tex], we need to determine the value of [tex]\( g(x) \)[/tex] when [tex]\( x = 0 \)[/tex]. The [tex]\( y \)[/tex]-intercept is the value of the function at this point.
Here are the steps:
1. Substitute [tex]\( x = 0 \)[/tex] into the function [tex]\( g(x) = (x-6)(x-3)(x+2) \)[/tex].
[tex]\[
g(0) = (0-6)(0-3)(0+2)
\][/tex]
2. Simplify the expression inside the parentheses:
[tex]\[
g(0) = (-6)(-3)(2)
\][/tex]
3. Multiply the values together:
[tex]\[
(-6) \times (-3) = 18
\][/tex]
[tex]\[
18 \times 2 = 36
\][/tex]
Therefore, the [tex]\( y \)[/tex]-intercept of the function [tex]\( g(x) = (x-6)(x-3)(x+2) \)[/tex] is [tex]\( 36 \)[/tex].
In other words, the point where the graph of the function intersects the [tex]\( y \)[/tex]-axis is [tex]\((0, 36)\)[/tex].
