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

The hole in this function exists at (3, 0).

To find a hole, you must find what first makes the bottom of the equation (the denominator) equal to 0.

x - 3 = 0

x = 3

Now knowing this, we plug 3 in to the top of the equation, to find the y value that will not be possible either.

x^2 - 9

3^3 - 9

9 - 9

0

Answer 2

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

First we will factor the numerator

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

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)