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Complete the Table. Find the values of y that correspond to the values of x when y = 6/x. 2. Solve the equations.

Mathematics

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Answer

To complete the table, we need to substitute each given value of xx into the equation y=6xy = \frac{6}{x} and calculate the corresponding value of yy.

Graph of y = 6/x

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Key points of y = 6/x
Pointxy

Step-by-step solution

2 steps
  1. Calculate yy for each xx value.

    • For x=−6x = -6: y=6−6=−1y = \frac{6}{-6} = -1
    • For x=−5x = -5: y=6−5=−1.2y = \frac{6}{-5} = -1.2
    • For x=−4x = -4: y=6−4=−1.5y = \frac{6}{-4} = -1.5
    • For x=−3x = -3: y=6−3=−2y = \frac{6}{-3} = -2
    • For x=−2x = -2: y=6−2=−3y = \frac{6}{-2} = -3
    • For x=−1x = -1: y=6−1=−6y = \frac{6}{-1} = -6
    • For x=0x = 0: y=60y = \frac{6}{0}, which is undefined.
    • For x=1x = 1: y=61=6y = \frac{6}{1} = 6
    • For x=2x = 2: y=62=3y = \frac{6}{2} = 3
    • For x=3x = 3: y=63=2y = \frac{6}{3} = 2
    • For x=4x = 4: y=64=1.5y = \frac{6}{4} = 1.5
    • For x=5x = 5: y=65=1.2y = \frac{6}{5} = 1.2
    • For x=6x = 6: y=66=1y = \frac{6}{6} = 1
  2. Complete the table with the calculated yy values.

    The completed table is:

    x−6−5−4−3−2−10123456y−1−1.2−1.5−2−3−6undefined6321.51.21\begin{array}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|} \hline x & -6 & -5 & -4 & -3 & -2 & -1 & 0 & 1 & 2 & 3 & 4 & 5 & 6 \\ \hline y & -1 & -1.2 & -1.5 & -2 & -3 & -6 & \text{undefined} & 6 & 3 & 2 & 1.5 & 1.2 & 1 \\ \hline \end{array}

    The completed table is shown above.

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