4.1 Quiz
100 points possible $\quad 0 / 8$ answered
Question 1
For the function $f(x)=3 \cdot 9^{x}$, calculate the following function values:
\[
\begin{array}{l}
f(-2)= \\
f\left(\frac{1}{2}\right)= \\
f(0)=
\end{array}
\]

Step 1 ：Substitute \(-2\) for \(x\) in the function \(f(x) = 3 \times 9^x\).

Step 2 ：Calculate \(f(-2) = 3 \times 9^{-2}\).

Step 3 ：Simplify to \(f(-2) = 3 / 9^2\).

Step 4 ：Further simplify to \(f(-2) = 3 / 81\).

Step 5 ：Finally, simplify to \(f(-2) = 1 / 27\).

Step 6 ：Substitute \(1/2\) for \(x\) in the function \(f(x) = 3 \times 9^x\).

Step 7 ：Calculate \(f(1/2) = 3 \times 9^{1/2}\).

Step 8 ：Simplify to \(f(1/2) = 3 \times \sqrt{9}\).

Step 9 ：Further simplify to \(f(1/2) = 3 \times 3\).

Step 10 ：Finally, simplify to \(f(1/2) = 9\).

Step 11 ：Substitute \(0\) for \(x\) in the function \(f(x) = 3 \times 9^x\).

Step 12 ：Calculate \(f(0) = 3 \times 9^0\).

Step 13 ：Simplify to \(f(0) = 3 \times 1\).

Step 14 ：Finally, simplify to \(f(0) = 3\).

Step 15 ：So, the function values are \(\boxed{f(-2) = 1/27}\), \(\boxed{f(1/2) = 9}\), and \(\boxed{f(0) = 3}\).