Question 2

For the function $f(x)=3 \cdot 4^{x}$, calculate the following function values:
\[
\begin{array}{l}
f(-2)= \\
f\left(\frac{1}{2}\right)= \\
f(0)=
\end{array}
\]

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Step 1 ：Substitute $-2$ for $x$ in the function $f(x)=3 \cdot 4^{x}$ to get $f(-2) = 3 \cdot 4^{-2}$

Step 2 ：Simplify $f(-2) = 3 \cdot 4^{-2}$ to $f(-2) = 3 \cdot \frac{1}{4^2}$

Step 3 ：Simplify $f(-2) = 3 \cdot \frac{1}{16}$ to $f(-2) = \frac{3}{16}$

Step 4 ：Substitute $\frac{1}{2}$ for $x$ in the function $f(x)=3 \cdot 4^{x}$ to get $f\left(\frac{1}{2}\right) = 3 \cdot 4^{\frac{1}{2}}$

Step 5 ：Simplify $f\left(\frac{1}{2}\right) = 3 \cdot 4^{\frac{1}{2}}$ to $f\left(\frac{1}{2}\right) = 3 \cdot 2$

Step 6 ：Simplify $f\left(\frac{1}{2}\right) = 3 \cdot 2$ to $f\left(\frac{1}{2}\right) = 6$

Step 7 ：Substitute $0$ for $x$ in the function $f(x)=3 \cdot 4^{x}$ to get $f(0) = 3 \cdot 4^{0}$

Step 8 ：Simplify $f(0) = 3 \cdot 4^{0}$ to $f(0) = 3 \cdot 1$

Step 9 ：Simplify $f(0) = 3 \cdot 1$ to $f(0) = 3$

Step 10 ：So, the function values are $f(-2) = \boxed{\frac{3}{16}}$, $f\left(\frac{1}{2}\right) = \boxed{6}$, and $f(0) = \boxed{3}$