1. The problem asks to determine if the function represented by the table is linear or nonlinear. 2. A function is linear if it can be expressed as $y = mx + b$, where $m$ and $b$ are constants, and the rate of change (slope) between any two points is constant. 3. Let's calculate the slope between consecutive points where both $x$ and $y$ values are given: - Between $(1,4)$ and $(4,9)$: $$m = \frac{9 - 4}{4 - 1} = \frac{5}{3}$$ - Between $(4,9)$ and $(1,-6)$: $$m = \frac{-6 - 9}{1 - 4} = \frac{-15}{-3} = 5$$ 4. Since the slopes $\frac{5}{3}$ and $5$ are not equal, the rate of change is not constant. 5. Therefore, the function is nonlinear because the slope between points changes. Final answer: The function is nonlinear.