26 Here is a table of values for $y = \frac{6}{x} - 2x$. | $x$ | -4 | -3 | -2 | -1 | 2 | 3 | 4 | |-----|----|----|----|----|---|---|---| | $y$ | 6.5| 4 | 1 | -4 | 1 | 4 | 6.5| (a) Draw the graph of $y = \frac{6}{x} - 2x$ for $-4 < x < 4, x \neq 0$. (b) Use your graph to find the positive solution of $\frac{6}{x} - 2x = 0$. Give your answer to 1 decimal place.

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26 Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 26 - 2023 - Paper 1

Question 26

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26 Here is a table of values for $y = \frac{6}{x} - 2x$. | $x$ | -4 | -3 | -2 | -1 | 2 | 3 | 4 | |-----|----|----|----|----|---|---|---| | $y$ | 6.5| 4 | 1 | -4 |... show full transcript

Worked Solution & Example Answer:26 Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 26 - 2023 - Paper 1

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, first, plot the points provided in the table of values. The x-values range from -4 to 4, excluding 0. The corresponding y-values are computed as follows:

For $x = -4$ , $y = \frac{6}{-4} - 2(-4) = 6.5$
For $x = -3$ , $y = \frac{6}{-3} - 2(-3) = 4$
For $x = -2$ , $y = \frac{6}{-2} - 2(-2) = 1$
For $x = -1$ , $y = \frac{6}{-1} - 2(-1) = -4$
For $x = 2$ , $y = \frac{6}{2} - 2(2) = 1$
For $x = 3$ , $y = \frac{6}{3} - 2(3) = 4$
For $x = 4$ , $y = \frac{6}{4} - 2(4) = 6.5$

Now, plot these points on a Cartesian plane and connect them with a smooth curve, ensuring that the curve approaches infinity as it nears the vertical asymptote at $x = 0$ .

Step 2

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

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Answer

To find the positive solution of $\frac{6}{x} - 2x = 0$ , we need to determine where the graph intersects the x-axis. From the graph, we can visually inspect the point where the curve crosses the x-axis for $x > 0$ . This appears to occur at approximately $x = 1.5$ . Thus, reporting this to one decimal place, we have:

$x = 1.5$ .

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26 Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 26 - 2023 - Paper 1

Worked Solution & Example Answer:26 Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 26 - 2023 - Paper 1

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

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

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