Answer
A) Linear
B) $ g(x) = 2x$
Work Step by Step
Given
$$
\begin{array}{c|c}
\hline x & g(x) \\
\hline 0 & 0 \\
1 & 2 \\
2 & 4 \\
3 & 6 \\
4 & 8 \\
\hline
\end{array}
$$
A) We know that a function is linear if the differences of successive values of the function is a constant. A function is exponential if the ratios of successive values of the function is a constant.
$$
\begin{aligned}
&g(1)-g(0)=2-0=2\\
&g(2)-g(1)=4-2=2
\end{aligned}
$$
Thus, the function is linear.
B) We know that
$$
g(x)=mx+b
$$
Thus,
$$
m=\frac{2-0}{1-0}=2
$$
The table shows that $x=0$ and $g(0) = 0= b$. Hence:
$$
\begin{aligned}
g(x)& =2x \\
\end{aligned}
$$
