The given graph is a graph of the absolute value function:
[tex]y=f(x)=|x|[/tex]
A graph of the function y=f(x) when translated horizontally by a units, vertically by b units, and horizontally stretched by a factor of k, where k>=1 is :
[tex]y=\frac{1}{k}f(x-a)+b[/tex]
The required graph in the choices is that of the function:
[tex]y=\frac{1}{3}f(x+5)-3[/tex]
This equation shows that the new function translates the previous one vertically down by 3 units (b=-3).
Horizontally to the left by 5 units (a=-5), and a horizontal stretch by a factor of 3 (k=3).
Hence, the new graph will be the one that gives the old graph translated vertically downwards by 3 units, horizontally to the left by 5 units, and a horizontal stretch away from the y-axis by a factor of 3.
The graph that best fits is shown below:
