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Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 7 - 2023 - Paper 4

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Here is a table of values for $y = \frac{6}{x} - 2x$. | x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 | |-----|----|----|----|----|----|----|----|----|----| | y... show full transcript

Worked Solution & Example Answer:Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 7 - 2023 - Paper 4

Step 1

Draw the graph of $y = \frac{6}{x} - 2x$ for $-4 < x < 4, x \neq 0$

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Answer

To draw the graph, plot the points provided in the table:

  • At x=−4x = -4, y=6.5y = 6.5.
  • At x=−3x = -3, y=4y = 4.
  • At x=−2x = -2, y=1y = 1.
  • At x=−1x = -1, y=1y = 1.
  • At x=1x = 1, y=4y = 4.
  • At x=2x = 2, y=1y = 1.
  • At x=3x = 3, y=−4y = -4.
  • At x=4x = 4, y=6.5y = 6.5.

Ensure that the curve approaches infinity as xx approaches 00 from the left and right, and has a defined behavior as x moves away from zero. The graph should clearly indicate that the function is not defined at x=0x = 0.

Step 2

Use your graph to find the positive solution of $\frac{6}{x} - 2x = 0$

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Answer

From the graph, identify the point where the curve intersects the x-axis (where y=0y=0). This gives the solution to the equation 6x−2x=0\frac{6}{x} - 2x = 0. After observing the graph, the positive x-value at the intersection appears to be approximately x=1.5x = 1.5. Thus, the positive solution is:

Answer: x=1.5x = 1.5.

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