Graphing a Rational Function and Solving Equations Graphically
Graphing a Rational Function and Solving Equations Graphically
Secondary 3
The variables \(x\) and \(y\) are connected by the equation\(y=\frac{{{x}^{2}}}{3}+\frac{2}{x}-1\).
Some corresponding values of \(x\) and \(y\) are given in the following table.
\(x\) | \(0.5\) | \(0.6\) | \(0.8\) | \(1.0\) | \(1.5\) | \(2.0\) | \(2.5\) | \(3.0\) |
|---|---|---|---|---|---|---|---|---|
\(y\) | \(3.08\) | \(2.45\) | \(p\) | \(1.33\) | \(1.08\) | \(1.33\) | \(1.88\) | \(2.67\) |
- Find the value of \(p\).
- Using the scale of \(4\) cm to \(1\) unit on each axis, draw a horizontal \(x\)-axis for \(0\le x\le 3\)and a vertical \(y\)-axis for \(0\le y\le 4\).
On your axes, plot the points given in the table and join them with a smooth curve.
- Use your graph to find two solutions of \(\frac{{{x}^{2}}}{3}+\frac{2}{x}-3=0\) in the range \(0\le x\le 3\).
- By drawing a tangent, find the gradient of the curve at the point \(\left( 1,1.33 \right)\).
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Answer:(a) \(1.71\). (c) \(x\approx0.70,2.57\). (d) About \(-1.33\).
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