In this problem, you're asked to sketch the graph of $y = f(-x)$ given the graph of $y = f(x)$.

Explanation:

• The graph of $y = f(-x)$ is a reflection of the graph of $y = f(x)$ across the y-axis.
• This transformation flips the graph horizontally. Every point $(x, y)$ on the original graph will be transformed to $(-x, y)$ in the new graph.

Steps:

1. Reflect every point of the given graph of $y = f(x)$ across the y-axis.
2. For example, the point at $(6, 7)$ on the original graph would move to $(-6, 7)$.
3. Repeat this reflection for all points and redraw the new graph.

Would you like me to generate the reflected graph visually? Let me know if you have any questions or if you'd like more details on any step!

Here are some follow-up questions you can explore:

1. How does the graph change if we replace $f(-x)$ with $-f(x)$?
2. What happens to the graph if we shift it vertically, say to $f(x) + 3$?
3. Can you describe how the transformation affects key points like intercepts or maxima/minima?
4. What if we combine transformations, like reflecting across the y-axis and then shifting up?
5. How can we verify algebraically that the reflected graph corresponds to $f(-x)$?

Tip: When transforming graphs, always think of the transformation rules: reflections, translations, stretches, or compressions.