Which of the following functions is graphed below?

a. y=x |x+3| -4

b. y=|x+3|+4

c. y=|x-3| +4

d. y=|x-3| -4

The answer is A. using the vertex as a reference point (-3, -4), we can identify the correct equation. in a typical y=|x| equation, the vertex is (0,0). therefore, we can see the graph is vertically shifted down 4 points. this means that the equation must have -4 in it. This narrows our options down to A and D. you can use the process of elimination and input the x value of the vertex into the equation to see if you get the correct y value. for d, |-3-3| -4 = 2, and for a, |3-3| - 4 = -4. since -4 is the correct y value, A is the correct option.

hope this makes sense... and i hope this helps!

Answers: the graph is translated down 1 unit and the domain and range of g(x) is the same as the domain and range of f(x).