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MakcuM [25]
1 year ago
15

q(x)= x 2 −6x+9 x 2 −8x+15 ​ q, left parenthesis, x, right parenthesis, equals, start fraction, x, squared, minus, 8, x, plus, 1

5, divided by, x, squared, minus, 6, x, plus, 9, end fraction Describe the behavior of the function qqq around its vertical asymptote at x=3x=3x, equals, 3.
Mathematics
1 answer:
AURORKA [14]1 year ago
8 0

According to the theory of <em>rational</em> functions, there are no <em>vertical</em> asymptotes at the <em>rational</em> function evaluated at x = 3.

<h3>What is the behavior of a functions close to one its vertical asymptotes?</h3>

Herein we know that the <em>rational</em> function is q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15), there are <em>vertical</em> asymptotes for values of x such that the denominator becomes zero. First, we factor both numerator and denominator of the equation to see <em>evitable</em> and <em>non-evitable</em> discontinuities:

q(x) = (x² - 6 · x + 9) / (x² - 8 · x + 15)

q(x) = [(x - 3)²] / [(x - 3) · (x - 5)]

q(x) = (x - 3) / (x - 5)

There are one <em>evitable</em> discontinuity and one <em>non-evitable</em> discontinuity. According to the theory of <em>rational</em> functions, there are no <em>vertical</em> asymptotes at the <em>rational</em> function evaluated at x = 3.

To learn more on rational functions: brainly.com/question/27914791

#SPJ1

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