f(x)=|x| help please

Question

then shifted 500 units to the right, vertically stretched by a factor of 5 then shifted down 750 units

 

 

 

Similiar to g(x)=-f(x)+10 (-15,10)(0,20)(20,50)

Answer 1

f(x)=|x| behaves like f(x)=x when x≥0 and like f(x)=-x when x<0.

This gives f(x) a V-shaped appearance where the point of the V is at the origin.

The transformations move the point of the V in various directions.

500 units to the right requires x to be replaced by x-500 so f(x)=|x-500|, while vertically stretched requires a multiplication of 5: f(x)=5|x-500|, and a vertical downward shift makes f(x)=5|x-500|-750.