Determine the type of the function f:
$\begin{array}{c}f(-5)=6 \\ f(-6)=-9\end{array}$

Step 1 ：Given the points (-5,6) and (-6,-9), we need to determine the type of the function f.

Step 2 ：First, we calculate the slope (a) of the line passing through the points (-5,6) and (-6,-9). The formula for the slope is \(a = \frac{y2 - y1}{x2 - x1}\).

Step 3 ：Substituting the given points into the formula, we get \(a = \frac{-9 - 6}{-6 - (-5)} = 15.0\).

Step 4 ：Next, we find the y-intercept (b) using the formula \(y = ax + b\). We can substitute one of the points and the slope into this formula to solve for b.

Step 5 ：Substituting the point (-5,6) and the slope 15.0 into the formula, we get \(b = 6 - 15.0 \times -5 = 81.0\).

Step 6 ：We then check if the calculated b value satisfies the other point (-6,-9). If it does, then the function is linear. If not, the function is not linear.

Step 7 ：Substituting the point (-6,-9) and the slope 15.0 and y-intercept 81.0 into the formula, we get \(-9 = 15.0 \times -6 + 81.0\), which is true. Therefore, the function is linear.

Step 8 ：Final Answer: The type of the function f is \(\boxed{linear}\).