Certainly! Let's complete the table by calculating the values of the function \(f(x) = x^2 + 3x - 5\) for each given \(x\).
Given:
[tex]\[ f(x) = x^2 + 3x - 5 \][/tex]
We will evaluate this function for each of the provided \(x\) values.
1. For \( x = 4 \):
[tex]\[ f(4) = 4^2 + 3 \cdot 4 - 5 = 16 + 12 - 5 = 23 \][/tex]
2. For \( x = 4.5 \):
[tex]\[ f(4.5) = (4.5)^2 + 3 \cdot 4.5 - 5 = 20.25 + 13.5 - 5 = 28.75 \][/tex]
3. For \( x = 4.9 \):
[tex]\[ f(4.9) = (4.9)^2 + 3 \cdot 4.9 - 5 = 24.01 + 14.7 - 5 = 33.71 \][/tex]
4. For \( x = 4.99 \):
[tex]\[ f(4.99) = (4.99)^2 + 3 \cdot 4.99 - 5 = 24.9001 + 14.97 - 5 = 34.8701 \][/tex]
5. For \( x = 4.999 \):
[tex]\[ f(4.999) = (4.999)^2 + 3 \cdot 4.999 - 5 = 24.990001 + 14.997 - 5 = 34.987001 \][/tex]
6. For \( x = 5.001 \):
[tex]\[ f(5.001) = (5.001)^2 + 3 \cdot 5.001 - 5 = 25.010001 + 15.003 - 5 = 35.013001 \][/tex]
7. For \( x = 5.01 \):
[tex]\[ f(5.01) = (5.01)^2 + 3 \cdot 5.01 - 5 = 25.1001 + 15.03 - 5 = 35.1301 \][/tex]
8. For \( x = 5.1 \):
[tex]\[ f(5.1) = (5.1)^2 + 3 \cdot 5.1 - 5 = 26.01 + 15.3 - 5 = 36.31 \][/tex]
9. For \( x = 5.5 \):
[tex]\[ f(5.5) = (5.5)^2 + 3 \cdot 5.5 - 5 = 30.25 + 16.5 - 5 = 41.75 \][/tex]
10. For \( x = 6 \):
[tex]\[ f(6) = 6^2 + 3 \cdot 6 - 5 = 36 + 18 - 5 = 49 \][/tex]
Now we fill in the table with these results:
[tex]\[
\begin{array}{|c|c|}
\hline
x & x^2 + 3x - 5 \\
\hline
4 & 23 \\
\hline
4.5 & 28.75 \\
\hline
4.9 & 33.71 \\
\hline
4.99 & 34.8701 \\
\hline
4.999 & 34.987001 \\
\hline
5.001 & 35.013001 \\
\hline
5.01 & 35.1301 \\
\hline
5.1 & 36.31 \\
\hline
5.5 & 41.75 \\
\hline
6 & 49 \\
\hline
\end{array}
\][/tex]
These are the calculated values of the function [tex]\(f(x) = x^2 + 3x - 5\)[/tex] for the given [tex]\(x\)[/tex] values.
