The problem asks: if $(7, 9)$ is a point on the graph of $y = f(x)$, which point must be on the graph of $y = f(-x)$?

Explanation:

When switching from $f(x)$ to $f(-x)$, it reflects the graph of the function across the y-axis. This reflection means that for every point $(x, y)$ on the graph of $y = f(x)$, the corresponding point on the graph of $y = f(-x)$ will be $(-x, y)$.

Given:

• The point $(7, 9)$ is on the graph of $y = f(x)$.

Therefore:

• The corresponding point on the graph of $y = f(-x)$ would be $(-7, 9)$.

Correct answer:

$(-7, 9)$

Would you like further details on function transformations, or do you have any questions? Here are some follow-up questions that could expand on this concept:

1. What is the impact of reflecting a function over the x-axis?
2. How would the graph change if the function is reflected across both the x-axis and y-axis?
3. What happens to a graph when you apply a vertical or horizontal shift?
4. Can reflections and shifts be combined in a single transformation?
5. What would the transformation be if the function is multiplied by a negative constant?

Tip: Always remember that replacing $x$ with $-x$ reflects the graph across the y-axis!