Hello!
This graph is known as a rational function, it's parent function is y = 1/x. This graph is unique because it has two asymptotes where the graph never crosses.
Looking at the graph, the graph did not shift five units upward, but five units to the left because the vertical asymptote is at x = -5, so therefore, it moved five units to the left.
Due to how it is shifted five units to the left, the graph is written as: y = 1/x - (-5), which is simplified to y = 1/(x + 5).
<u>Final answers</u>:
- Parent function: y = 1/x
- Transformations: A vertical shift of five units to the left (fourth choice).
- Graphed function: y = 1/(x + 5)
