The given function is $f(x) = 3^x - 1$, and you are asked to evaluate it at several points, rounding the answers to three decimal places. Let's go over the calculations for the specific values:

1. $f\left(\frac{1}{2}\right)$

$f\left(\frac{1}{2}\right) = 3^{\frac{1}{2}} - 1 = \sqrt{3} - 1 = 1.732 - 1 = 0.732$

2. $f(2.5)$

$f(2.5) = 3^{2.5} - 1 = 15.588 - 1 = 14.588$

3. $f(-1)$

$f(-1) = 3^{-1} - 1 = \frac{1}{3} - 1 = 0.333 - 1 = -0.667$

4. $f\left(\frac{1}{4}\right)$

$f\left(\frac{1}{4}\right) = 3^{\frac{1}{4}} - 1 = \sqrt[4]{3} - 1 \approx 1.316 - 1 = 0.316$

Now that we have calculated the values, let's compare:

1. $f\left(\frac{1}{2}\right) = 0.732$ (Not 0)
2. $f(2.5) = 14.588$ (Not 5.20)
3. $f(-1) = -0.667$ (Not $\frac{1}{49}$)
4. $f\left(\frac{1}{4}\right) = 0.316$ (Not 0)

It looks like the answers given were incorrect, and the correct values are as calculated above.

Would you like more details on any of the steps? Here are some follow-up questions:

1. How does the function $3^x$ behave for different values of $x$?
2. Why does $3^x$ grow exponentially for positive $x$?
3. Can you explain why negative values of $x$ result in fractions for $3^x$?
4. What would happen if $x$ is a very large negative number?
5. How does rounding affect your final results when evaluating functions?

Tip: When calculating powers of non-integer exponents, using a scientific calculator ensures accuracy.