1. **Stating the problem:** We are given discrete points: $(-3,9)$, $(-3,5)$, $(-1,2)$, $(0,2)$, $(1,1)$, $(3,1)$ and asked to identify the function type they represent. 2. **Understanding function types:** - A **linear function** has the form $y = mx + b$ and produces a straight line. - A **quadratic function** has the form $y = ax^2 + bx + c$ and produces a parabola. - An **exponential function** has the form $y = ab^x$ where $b > 0$ and $b \neq 1$. 3. **Checking for linearity:** Calculate differences in $y$ for equal steps in $x$: - From $x=-1$ to $x=0$, $y$ stays at 2. - From $x=0$ to $x=1$, $y$ decreases from 2 to 1. - From $x=1$ to $x=3$, $y$ stays at 1. The $y$ values do not change consistently with $x$, so not linear. 4. **Checking for quadratic:** Quadratic functions have a symmetric pattern and a single $y$ value for each $x$. Here, $x=-3$ has two different $y$ values (9 and 5), which violates the definition of a function. 5. **Checking for exponential:** Exponential functions have one $y$ value per $x$ and grow or decay multiplicatively. Here, multiple $y$ values for $x=-3$ and inconsistent pattern mean it is not exponential. 6. **Conclusion:** Since the data points do not fit linear, quadratic, or exponential function types and violate the function definition by having multiple $y$ values for the same $x$, the correct answer is **Neither**.