1. **State the problem:** We are given a table of values for a function $f(x)$ and need to determine what type of function it could represent. 2. **Given values:** $$\begin{array}{c|ccccc} x & -2 & -1 & 0 & 1 & 2 \\ f(x) & 0.25 & 0.5 & 1 & 2 & 4 \\\end{array}$$ 3. **Check if the function is cubic:** A cubic function has the form $$f(x) = ax^3 + bx^2 + cx + d$$ which generally does not produce values doubling consistently as $x$ increases by 1. 4. **Check if the function is exponential:** An exponential function has the form $$f(x) = a \cdot b^x$$ where $a$ is the initial value and $b$ is the base. 5. **Test exponential pattern:** Calculate the ratio between consecutive $f(x)$ values: $$\frac{f(-1)}{f(-2)} = \frac{0.5}{0.25} = 2$$ $$\frac{f(0)}{f(-1)} = \frac{1}{0.5} = 2$$ $$\frac{f(1)}{f(0)} = \frac{2}{1} = 2$$ $$\frac{f(2)}{f(1)} = \frac{4}{2} = 2$$ Since the ratio is constant (2), the function doubles for each increase of 1 in $x$, confirming an exponential function. 6. **Find $a$ and $b$:** Using $f(0) = 1$, we get $$f(0) = a \cdot b^0 = a = 1$$ So the function is: $$f(x) = 1 \cdot 2^x = 2^x$$ **Final answer:** The function is exponential (option B).