Answer:
y = 2|x| - 3
Explanation:
We'll start with our parent function which is y = |x|. Notice that graph is translated down by 3 units. So, we'll add that:
Also notice that the ordered pair (1, -1) is on the graph. |1| = 1, so a translation of -3 should take it to -2 and it should have been (1, -2). But, it's not so it must be that the graph is stretched/compressed. If you multiply every point by 2, it gives us the result we want. Say for example, f(1) = 2|1| - 3 = 2 - 3 = -1. We get the point (1, -1) which is exactly what we want. We write compressions as (where a is the compression/stretching constant):
Our compression constant is 2, so our final answer is:
y = 2|x| - 3.