To find the values of [tex]\( f(x) = \frac{x-1}{x+3} \)[/tex] for the given [tex]\( x \)[/tex] values, we will substitute each [tex]\( x \)[/tex] into the function and simplify the expression. Let's go through each step-by-step:
- For [tex]\( x = -10 \)[/tex]:
[tex]\[
f(-10) = \frac{-10-1}{-10+3} = \frac{-11}{-7} = 1.5714285714285714
\][/tex]
- For [tex]\( x = -8 \)[/tex]:
[tex]\[
f(-8) = \frac{-8-1}{-8+3} = \frac{-9}{-5} = 1.8
\][/tex]
- For [tex]\( x = -6 \)[/tex]:
[tex]\[
f(-6) = \frac{-6-1}{-6+3} = \frac{-7}{-3} = 2.3333333333333335
\][/tex]
- For [tex]\( x = -4 \)[/tex]:
[tex]\[
f(-4) = \frac{-4-1}{-4+3} = \frac{-5}{-1} = 5.0
\][/tex]
- For [tex]\( x = -3.5 \)[/tex]:
[tex]\[
f(-3.5) = \frac{-3.5-1}{-3.5+3} = \frac{-4.5}{-0.5} = 9.0
\][/tex]
The value for [tex]\( x = -2.5 \)[/tex] is not provided in the problem statement. We can proceed with the provided values.
- For [tex]\( x = -2 \)[/tex]:
[tex]\[
f(-2) = \frac{-2-1}{-2+3} = \frac{-3}{1} = -3.0
\][/tex]
- For [tex]\( x = 0 \)[/tex]:
[tex]\[
f(0) = \frac{0-1}{0+3} = \frac{-1}{3} = -0.3333333333333333
\][/tex]
- For [tex]\( x = 2 \)[/tex]:
[tex]\[
f(2) = \frac{2-1}{2+3} = \frac{1}{5} = 0.2
\][/tex]
- For [tex]\( x = 4 \)[/tex]:
[tex]\[
f(4) = \frac{4-1}{4+3} = \frac{3}{7} = 0.42857142857142855
\][/tex]
Now we can fill out the table with these calculated values:
[tex]\[
\begin{array}{|c|c|}
\hline
x & f(x) \\
\hline
-10 & 1.5714285714285714 \\
\hline
-8 & 1.8 \\
\hline
-6 & 2.3333333333333335 \\
\hline
-4 & 5.0 \\
\hline
-3.5 & 9.0 \\
\hline
-2.5 & - \\
\hline
-2 & -3.0 \\
\hline
0 & -0.3333333333333333 \\
\hline
2 & 0.2 \\
\hline
4 & 0.42857142857142855 \\
\hline
\end{array}
\][/tex]
