find an equation for the rational graphed Find an equation f

Find an equation for the rational function graphed below.

Solution

From the graph, we observe that:

i) x = -3 is a verical asymptote. Therefore, ( x + 3) must be a factor of the denominator.

ii) There is a hole at x = 2. Therefore (x -2) must be a factor of both the numerator and the denominator.

iii) y = 1 is a horizontal asymptote. Therefore, the degree of the numerator and the denominator will be same. Also, the leading coefficient of the numerator will be 1.

iv) x = -1 is a zero of the rational function. Therefore (x +1) must be a factor of the numerator.

In view of the above, the equation of the rational function is f(x) = (x - 2)( x+1)/( x-2)( x+3)