Question

Write a rule y=f(x) that would produce the graph.

Answer 1

y = | x+2 | -1

Explanation:

The absolute value function is shifted left 2 units and down 1. That makes it ...

y = abs(x+2) -1

Using the usual symbols for absolute value:

y = |x+2| -1

_____

The translation transformation is ...

y = f(x -a) +b

to translate the graph of f(x) right by "a" units and up by "b" units. Here, we have a translation left 2 and down 1, so a=-2, b=-1. The original function is the absolute value function in this case.