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

`\boxedx-5`