if $f(x)=3|x - 4|+6$, what is the y - intercept?\na. $(0,-6)$\nb. $(0,9)$\nc. $(0,18)$\nd. $(0,4)$

Explanation:

Step1: Recall the definition of y - intercept

The y - intercept of a function (y = f(x)) is the value of (y) when (x = 0).

Step2: Substitute (x = 0) into the function

Given (f(x)=3|x - 4|+6), substitute (x = 0): [ \begin{align*} f(0)&=3|0 - 4|+6\ &=3\times| - 4|+6\ &=3\times4+6\ &=12 + 6\ &=18 \end{align*} ]

Answer:

C. ((0,18))