Question

in the table, ( y_1 ) is defined by a rational function of the form ( \frac{x - p}{x - q} ).( p = 2 )( q = square )use the table to find the values of ( p ) and ( q ).

x	( y_1 )
1	0.5
2	0
3	error
4	2
5	1.5
6	1.3333

Explanation:

Step1: Recall the error condition

A rational function \(\frac{x - p}{x - q}\) has an error (undefined) when the denominator is zero, i.e., \(x - q = 0\) or \(x = q\). From the table, when \(x = 3\), there is an error, so \(q = 3\). We can verify this with other points.

Step2: Verify with a point (optional)

Let's use \(x = 0\), \(Y_1=\frac{0 - p}{0 - q}=\frac{-p}{-q}=\frac{p}{q}\). We know \(p = 2\), so \(\frac{2}{q}=0.66666\approx\frac{2}{3}\), which confirms \(q = 3\). Also, for \(x = 4\), \(\frac{4 - 2}{4 - 3}=\frac{2}{1}=2\), which matches the table.

Answer:

\(q = 3\)