a) To write the figure number and the corresponding number of dots:
b) To identify the type of relation between the figure number and the number of dots in a figure:
For the first figure,
1+3+1=5
For the second figure,
[tex]\begin{gathered} 1+3+3+1=1+3(2)+1 \\ =8 \end{gathered}[/tex]
For the third figure,
[tex]\begin{gathered} 1+3+3+3+1=1+3(3)+1 \\ =11 \end{gathered}[/tex]
For the fourth figure,
[tex]\begin{gathered} 1+3+3+3+3+1=1+3(4)+1 \\ =14 \end{gathered}[/tex]
c) To tell whether this relation is a function or not:
Yes, it is a function.
d) To explain part (c) and find the algebraic expression:
For every n ( figure number) value, there is a unique D (number of dots) value.
So, this relation represents the function.
Then, the algebraic expression is,
[tex]D=2+3(n),\text{ where n is the natural numbers}[/tex]
