Question

1. (f(x)=|3x + 2|+ 4); translation 3 units down

Explanation:

Step1: Recall translation rule

For a function $y = f(x)$, a translation $k$ units down is given by $y=f(x)-k$.

Step2: Apply the rule

Here $f(x)=|3x + 2|+4$ and $k = 3$. So the new function is $y=(|3x + 2|+4)-3$.

Step3: Simplify the function

$y=|3x + 2|+4 - 3=|3x+2| + 1$.

Answer:

$y = |3x + 2|+1$