Question

Write a formula for the function g(x) obtained when the graph of f(x)=|x| is shifted down 10 units and to the right 12 units.

Answer 1

Explanation:

Do it one step at a time. Down is easier

g(x) = abs(x) - 10

Shifting it right is a little trickier. To make it shift right, you need to put a negative value after x. That's true of any function.

g(x) = abs(x - 12) - 10

That 12 looks awfully strange, but it is correct. You want to put a value in for x that make x - 12 = 0 so that all you are left with is -10 which is the minimum.

I have made the graph for you, so you can see that this is true.