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A function table is a tool that displays a set of values showing the relationship between input and output. It helps in understanding how a function works by listing potential inputs and their corresponding outputs.
In the context of this exercise, the table lists values for the function \( g(y) \) with the output values ranging from -10 to 10 as function inputs vary from -10 to 10. You can easily identify how each input \( y \) is related to an output \( g(y) \). For instance, when \( y = 0 \), \( g(y) = 5 \), demonstrating the table's use in quickly finding corresponding values.
Function tables are helpful for grasping the connection between variables in a function, making it easier to evaluate and analyze the data presented.

This exercise involves solving problems by finding missing values based on the function table. The key steps include understanding the relationship shown and applying it to solve for unknowns.
In part (a), you start with \( g(0) \) and look at the table to find when \( y = 0 \) so you know \( g(y) = 5 \). In (b), the problem requires finding a \( y \) value that results in \( g(y) = 0 \). According to the table, this corresponds to \( y = -5 \).
The exercise involves logical reasoning and the ability to trace relationships, allowing for the solution of equations. Function tables are systematic tools that simplify identifying the link between variables and outputs, which is crucial for problem solving.

Function evaluation is the process of calculating the output of a function for a specific input. It involves substituting the given input into the function and computing the output based on the relationship described by the function.
In this exercise, evaluating functions using the table is straightforward. For example, \( g(-5) \) is evaluated by identifying the matching input in the table, which is simply looking under the column labeled -5 and finding the corresponding output: 0. Similarly, you replace placeholders \( g(?) \) by reviewing the table to find desired outputs, such as -5, which occurs at \( y = -10 \).
This concept is foundational for understanding how different variables interact within a function, allowing you to effectively calculate specific results and ensure accuracy in mathematical functions.