Question

HELP !!!!! ASAP 4 ENDGENUITY Let the graph of g be a translation 5 units to the right followed by a translation 7 units down of the graph of f(x) = ∣x∣. Write g(x).

Answer 1

A translation of $h$ units upwards and $q$ units to the right is represented by the transformation

$(x,y)\rightarrow(x-q,y-h)$

So, to translate 5 right and 7 down, we need

$(x,y)\rightarrow(x-5,y+7)$

Now we just need to plug x=x-5 and y=y+7 in our equation (remember f(x)=y):

$y+7=|x-5|\\y=|x-5| - 7$

The answer is

$\boxed{g(x) = |x-5|-7}$