Question

What are the coordinates of the hole in the graph of the function f (x)

f (x) = x^2 - 9 / x - 3

_ , _

Answer 1

To find the coordinates of the hole in the graph of the function f(x)

First we will factor the numerator


`f(x) = \frac{ {x}^(2) - 9}{x - 3} \\ \\ = \frac{( {x}^(2) - {3}^(2) )}{x - 3} \\ \\ = ((x - 3)(x + 3))/((x - 3)) \\ \\ = x + 3`

The hole is where x - 3= 0,
i.e. at x = 3

x = 3

Therefore,
y = x² - 9
= 9 - 9
= 0

The hole is (3, 0)