To determine which points do not lie on the graph of the function y = log3(x), we need to analyze the properties of logarithmic functions.
Logarithmic functions are defined only for positive values of x. This means that any point with an x-coordinate that is less than or equal to zero will not lie on the graph. Additionally, since the base of the logarithm (which in this case is 3) influences the value of the logarithm, we must ensure the y-coordinates correspond correctly with their respective x-coordinates according to the log function.
For example, if a point is given as (1, 0), it would be on the graph since log3(1) = 0. However, a point like (-1, y) cannot be on the graph because log3(-1) is undefined. Therefore, any point with an x-value that is not positive does not belong to the graph.
To sum it up, to identify points that do not lie on the graph, look for:
- Points with x ≤ 0
- Points where y does not equal log3(x) for valid x-values
In conclusion, carefully evaluate the provided points against the domain and behavior of the logarithmic function to determine which does not belong.