The worksheet asks to complete the graphs given the knowledge that one is for an even function and the other is for an odd function. Here's how we can complete them:

1. Even Function:

• An even function has y-axis symmetry, meaning it mirrors itself over the y-axis.
• The provided half of the graph on the left shows a curve that is symmetric on the right side of the y-axis. To complete the graph, reflect the curve on the left side of the y-axis, ensuring that the shape mirrors the existing curve.

2. Odd Function:

• An odd function has origin symmetry, meaning if you rotate the graph 180° about the origin, the graph remains the same.
• The provided half of the graph on the right shows a curve. To complete the graph, you need to reflect it across the origin (both in the x and y directions), ensuring that the curve behaves symmetrically in that way.

Let me know if you would like more details on how to draw this or if you have further questions!

Follow-up Questions:

1. What is the mathematical definition of an even function?
2. What is the mathematical definition of an odd function?
3. How would the transformation rules apply to a graph that is neither even nor odd?
4. What are some examples of common even and odd functions?
5. How does origin symmetry affect the points in the graph of an odd function?

Tip: For odd functions, you can always verify origin symmetry by checking if $f(-x) = -f(x)$.