state a function rule for the number of dots in each figure

Answer:
[tex]g(x)=x^{2}[/tex]
Step-by-step explanation:
Since we know that a function gives exactly one output for a given input.
We can see that number of points in our diagram are 1,4 and 9.
These numbers represent a quadratic function as:
[tex]1^{2} =1[/tex]
[tex]2^{2} =4[/tex]
[tex]3^{2} =9[/tex]
Therefore, we can represent these points in a function as [tex]g(x)=x^{2}[/tex], where x is number of points.