Answer
Model: $f(x) = 3.2x-15$
Domain: All real numbers
Range: All real numbers
Work Step by Step
First make a scatter plot to determine the model type. Our scatter plot shows that the data is linear. Therefore find the slope of the line using any two points in the table. Take for example, $(-2, -21.4)\ ,\ (0,-15)$. $$\begin{aligned}
m&= \frac{y_2-y_1}{x_2-x_1}\\
&= \frac{-15-(-21.4)}{0-(-2)}\\
&= \frac{6.4}{2}\\
&= 3.2
\end{aligned}$$ Find the equation of the line. Use the point $(6,4.2)$: $$\begin{aligned}
y-y_1&= m(x-x_1)\\
y+4.2&= 3.2(x-6)\\
y&= 3.2x-19.2-4.2\\
y &= 3.2x-15
\end{aligned}$$ Hence the model is $$ f(x) = 3.2x-15.$$ The domain and range are:
Domain: All real numbers
Range: All real numbers
