For the function, supply a valid technology formula.
r(x) = 80

1 +
1
3.8
4x

r(x) =
Use technology to compute the missing values in the table accurate to four significant digits.
x	−3	−2	−1	0	1	2	3
r(x)

The given function is written as:

\[
r(x) = 80 \left( 1 + \frac{1}{3.8 + 4x} \right)
\]

We need to compute the values of \(r(x)\) for different values of \(x\) (-3, -2, -1, 0, 1, 2, 3), rounding each result to four significant digits.

First, I'll calculate the values of \(r(x)\) for each \(x\) using this formula.

Let me compute these values for you.Here are the computed values of \( r(x) \) for the given \( x \)-values, accurate to four significant digits:

\[
\begin{array}{c|c}
x & r(x) \\
\hline
-3 & 70.24 \\
-2 & 60.95 \\
-1 & -320.0 \\
0 & 101.1 \\
1 & 90.26 \\
2 & 86.78 \\
3 & 85.06 \\
\end{array}
\]

Would you like further clarification on the calculation or a deeper explanation of how the formula works?

Here are 5 relative questions you could explore:

1. How does the denominator \( 3.8 + 4x \) affect the values of \( r(x) \)?
2. Why does \( r(x) \) produce a large negative value at \( x = -1 \)?
3. How would the values change if the coefficient 80 was replaced by another number?
4. What happens to the function \( r(x) \) as \( x \to \infty \)?
5. Can this function model any real-world situations, and if so, how?

**Tip**: When evaluating functions with varying denominators, always check for potential undefined values, especially when division by zero could occur.

For the function, supply a valid technology formula.
r(x) = 80(1 + 1 / (3.8 + 4x))
Use technology to compute the missing values in the table accurate to four significant digits.
x = [−3, −2, −1, 0, 1, 2, 3]

Learn how to calculate values of the rational function r(x) = 80(1 + 1 / (3.8 + 4x)) for different x values. Explore concepts in algebra and numerical computation to solve this problem, rounding results to four significant digits. Suitable for high school students in Grades 10-12.

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