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

[tex](3, \infty )[/tex]

EXPLANATION

The given function is

[tex]f(x) = \frac{ {x}^{2} - 9}{x - 3} [/tex]

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

[tex]f(3) = \frac{0}{0} [/tex]

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

We need to simplify the function to obtain,

[tex]f(x) = \frac{(x - 3)(x + 3)}{(x - 3)} [/tex]

This implies that,

[tex]f(x) = x + 3[/tex]

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

To graph

[tex]f(x) = \frac{ {x}^{2} - 9}{x - 3} [/tex]
we draw the graph of

[tex]f(x) = x + 3[/tex]
and leave a hole at x=3.

See diagram in attachment.

Hence the coordinates of hole is

[tex](3, \infty )[/tex]

What are the coordinates of the hole in the graph of the function f(x) ? f(x)=x2−9x−3 Enter your answer in the boxes.

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

f(x)=x2−9x−3

Enter your answer in the boxes.