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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).

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A translation of [tex]h[/tex] units upwards and [tex]q[/tex] units to the right is represented by the transformation

[tex](x,y)\rightarrow(x-q,y-h)[/tex]

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

[tex](x,y)\rightarrow(x-5,y+7)[/tex]

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

[tex]y+7=|x-5|\\y=|x-5| - 7[/tex]

The answer is

[tex]\boxed{g(x) = |x-5|-7}[/tex]

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