To find the [tex]\( y \)[/tex]-intercept of the function, we need to determine the value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex]. The [tex]\( y \)[/tex]-intercept is the point where the graph of the function crosses the [tex]\( y \)[/tex]-axis.
Given the function:
[tex]\[ y = \frac{3x - 6}{x + 2} \][/tex]
We substitute [tex]\( x = 0 \)[/tex] into the equation to find the [tex]\( y \)[/tex]-intercept:
[tex]\[ y = \frac{3(0) - 6}{0 + 2} \][/tex]
Simplify the expression inside the equation:
[tex]\[ y = \frac{0 - 6}{2} \][/tex]
[tex]\[ y = \frac{-6}{2} \][/tex]
[tex]\[ y = -3 \][/tex]
Thus, the [tex]\( y \)[/tex]-intercept is:
[tex]\[ (0, -3) \][/tex]
The value of [tex]\( y \)[/tex] when [tex]\( x = 0 \)[/tex] is [tex]\(-3\)[/tex]. Therefore, the graph crosses the [tex]\( y \)[/tex]-axis at the point [tex]\((0, -3)\)[/tex].
