Answer
$g(x)$ is linear
$f(x)$ is exponential
Work Step by Step
A)
The rate of change of the functions on the interval $2 \leq x \leq 8$ are given below.
$$
\begin{aligned}
\text{For }f(x):&\frac{f(8)-f(2)}{8-2}\\
&=\frac{4.299-1.728}{6}\\
&=\frac{2.571}{6}\\
&=0.4285 \\
\text{ For }g(x):&\frac{g(8)-g(2)}{8-2}\\
&=\frac{5.088-1.464}{6}\\
&=\frac{3.624}{6}\\
&=0.604
\end{aligned}
$$
and on the interval $8 \leq x \leq 11$:
$$
\begin{aligned}
\text{For }f(x):&\frac{f(11)-f(8)}{11-8}\\
&=\frac{7.43-4.299}{3}\\
&=\frac{3.131}{3}\\
&=1.044\\
\text{For }g(x):&\frac{g(11)-g(8)}{11-8}\\
&=\frac{6.9-5.088}{3}\\
&=\frac{1.812}{3}\\
&=0.604
\end{aligned}
$$
B)
From our calculations, we see that $g(x)$ is linear since the rate of change is constant. The function, $f(x)$ must be exponential.
