Final answer:
To complete the table for an even function, use the property y(x) = y(-x) to find f(x) for negative inputs by reflecting the values given for positive inputs across the y-axis.
Step-by-step explanation:
The student is asking for help with completing a table using the properties of even functions. An even function is characterized by symmetry about the y-axis, following the property y(x) = y(-x). To complete the table, we can use this property to find the missing values for negative inputs. For example, if the function gives f(1) = 5, then f(-1) must also be 5 because an even function is symmetric concerning the y-axis.
Here are the steps you should follow:
Identify the given positive x values and their corresponding f(x) values from the table.For each positive x value, write down the corresponding negative x value.Use the property of even functions (y(x) = y(-x)) to determine the f(x) values for these negative x inputs.
Fill in the table with these calculated values.
This approach works because even functions exhibit symmetry, meaning the function's value at a positive x is the same as its value at the negative of that x (i.e., f(x) = f(-x)). Therefore, the table will be completed by mirroring the given values across the y-axis.