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To complete the table, we calculate the values for 3x-2, x+1, and y = (3x−2)/(x+1) for each given x value.

Mathematics

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Graph of y = (3x − 2)/(x + 1)

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Key points of y = (3x − 2)/(x + 1)
Pointxy
y-intercept0−2
x-intercept0.670

Here's the completed table for question 8(a):

To complete the table, we calculate the values for 3x−23x-2, x+1x+1, and y=3x−2x+1y = \frac{3x-2}{x+1} for each given xx value.

For x=−1x = -1:
3x−2=3(−1)−2=−3−2=−53x-2 = 3(-1)-2 = -3-2 = -5
x+1=−1+1=0x+1 = -1+1 = 0
y=−50y = \frac{-5}{0}, which is undefined.

The completed table is as follows:

x−4−3−2−10123453x−2−14−11−8−5−21471013x+1−3−2−10123456y=3x−2x+14.675.58−−20.51.331.7522.17\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|} \hline x & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 \\ \hline 3x-2 & -14 & -11 & -8 & -5 & -2 & 1 & 4 & 7 & 10 & 13 \\ \hline x+1 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline y = \frac{3x-2}{x+1} & 4.67 & 5.5 & 8 & - & -2 & 0.5 & 1.33 & 1.75 & 2 & 2.17 \\ \hline \end{array}
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