50 POINTS!!! Need Answer ASAP!

Mathematics

1 answer:

Andreyy893 years ago

3 0

The key features of polynomials are the vertex, axis of symmetry, x and y intercepts.

1. The degree will help you find the end behavior.

2. The vertex shows you where it changes concavity.

3. X and y intercepts give you a couple of points of reference.

4. Axis of symmetry is only applicable to even degree polynomials.

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

Vinvika [58]

ANSWER

$(3, \infty )$

EXPLANATION

The given function is

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

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

$f(3) = \frac{0}{0}$

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

We need to simplify the function to obtain,

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

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

$(3, \infty )$