It looks like you uploaded an image showing the graph of a rational function with some instructions to complete. I can help you with that!

Let's analyze the graph based on the information you provided in the image:

1. Parent function: The graph looks like a rational function, which is often a transformation of the basic rational function $f(x) = \frac{1}{x}$.

2. Reflection: The graph is reflected over the x-axis, as indicated by the "reflected over x-axis" statement. This means the original graph of $\frac{1}{x}$ has been flipped vertically.

3. Horizontal shift: The graph is moved 6 units to the right. This corresponds to a horizontal shift of $+6$ units in the equation, which modifies the parent function.

4. Vertical shift: The graph is moved 3 units upwards. This corresponds to a vertical shift of $+3$ units.

So, combining all these transformations into the equation form:

Equation for the graph: The equation should be written as: $y = -\frac{1}{x - 6} + 3$ Where:

• The negative sign indicates the reflection over the x-axis,
• The $-6$ inside the denominator represents the horizontal shift of 6 units to the right,
• The $+3$ outside the function indicates the vertical shift of 3 units upward.

Would you like further explanations on this transformation process or any specific part of the question?

Related questions:

1. How does the vertical asymptote change when there is a horizontal shift?
2. What happens to the horizontal asymptote after a vertical shift?
3. How would the equation change if the graph had been reflected over the y-axis?
4. What other types of transformations can be applied to rational functions?
5. How do horizontal and vertical shifts affect the domain and range of the function?

Tip: When analyzing transformations of rational functions, always remember that the transformations inside the function (such as $x - h$) are horizontal shifts, and those outside (like $+k$) are vertical shifts.