Here is a table of values for $y = \frac{6}{x} - 2x$ - OCR - GCSE Maths - Question 7 - 2023 - Paper 4
Question 7
Here is a table of values for $y = \frac{6}{x} - 2x$.
| x | -4 | -3 | -2 | -1 | 0 | 1 | 2 | 3 | 4 |
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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 from the table provided. For each value of x, calculate the corresponding y using the formula:
For x=−4: y=−46−2(−4)=−1.5+8=6.5
For x=−3: y=−36−2(−3)=−2+6=4
For x=−2: y=−26−2(−2)=−3+4=1
For x=−1: y=−16−2(−1)=−6+2=−4
For x=1: y=16−2(1)=6−2=4
For x=2: y=26−2(2)=3−4=−1
For x=3: y=36−2(3)=2−6=−4
For x=4: y=46−2(4)=1.5−8=−6.5
Next, plot these points on a graph and connect them smoothly. Remember to exclude the point where x=0 due to its undefined nature in the equation.
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, look for the intersection of the graph with the x-axis (where y=0). Based on the graph, identify the x-value at which the curve crosses the x-axis. Estimate this point to be approximately x=1.5. Round this value to one decimal place, giving the final answer as:
