Question

Write a function g whose graph represents the indicated transformation of the graph of f. The equation f (x) = |4+3| + 2 translated 2 units down is g (x) = ?

Answer 1

You have the following function f(x):

$f(x)=\left|4x-3\right|+2$

When you translate a function f(x) in b units, the new function can be described as follow:

$g(x)=f(x)+b$

where b is a number, positive or negative. It is positive if the translation is upward, it is negative if the translation is downward. In this case you have that the translation is 2 units downward, then, you obtain for the new function g(x):

$\begin{gathered} g(x)=f(x)-2 \\ g(x)=\left|4x-3\right|+2-2 \\ g(x)=\left|4x-3\right| \end{gathered}$