Final answer:
When given a table of values, finding the function involves examining patterns and relationships between input and output values. The function can be linear if the difference between input values is constant, or exponential if the ratio between input and output values is constant.
Step-by-step explanation:
When given a table of values, you can find the function by examining the patterns and relationships between the input values (x) and the corresponding output values (y). One way to do this is by looking for a consistent rate of change. If the difference between consecutive input values is the same, the function is likely linear. For example, if the input values increase by 1 each time and the output values increase by 3 each time, the function could be y = 3x. Another way to find the function is by looking for a consistent ratio between the input and output values. If the ratio is always the same, the function is likely exponential. For example, if the output values double each time the input values increase by 1, the function could be y = 2^x.