Question

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

f(x)=x2−9x−3



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Answer 1

ANSWER


`(3, \infty )`

Step-by-step explanation

The given function is


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

When we plug in x=3 into this function, we obtain,


`f(3) = (0)/(0)`

This means that the function is discontinuous at x=3.

We need to simplify the function to obtain,


`f(x) = ((x - 3)(x + 3))/((x - 3))`

This implies that,


`f(x) = x + 3`

The graph this function is a straight line that is continuous everywhere.

To graph


`f(x) = \frac{ {x}^(2) - 9}{x - 3}`
we draw the graph of


`f(x) = x + 3`
and leave a hole at x=3.

See diagram in attachment.

Hence the coordinates of hole is


`(3, \infty )`