To find the equation of [tex]\( g(x) \)[/tex] given the transformations applied to the original function [tex]\( f(x) = -3x \)[/tex], let's break down each step and transformation:
1. Vertical Stretch by Factor of 4:
- If we stretch [tex]\( f(x) \)[/tex] vertically by a factor of 4, we multiply the function by 4. Thus, the new function becomes:
[tex]\[
g1(x) = 4 \cdot f(x) = 4 \cdot (-3x) = -12x
\][/tex]
2. Translation 4 Units to the Right:
- Translating the function [tex]\( g1(x) \)[/tex] 4 units to the right means we replace [tex]\( x \)[/tex] with [tex]\( x - 4 \)[/tex] in the equation. So:
[tex]\[
g(x) = g1(x - 4) = -12(x - 4)
\][/tex]
3. Simplify the Equation:
- Finally, we simplify the equation obtained:
[tex]\[
g(x) = -12(x - 4) = -12x + 48
\][/tex]
Therefore, the equation for [tex]\( g(x) \)[/tex] after the given transformations is:
[tex]\[
\boxed{-12x + 48}
\][/tex]
