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
AURORKA [14]
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
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Answer:
Graph is attached :)
Step-by-step explanation:
Hope that helps!
Answer:
QR=RS=QS=29
Step-by-step explanation:
Given QRS is an equilateral triangle, thus all the three sides of the given triangle will be equal.
Also, from the given statement, we have
QR=2x-7, RS=5x-61 and QS=11+X
Now, As all the sides of the triangle are equal, therefore
QR=RS=QS
⇒QR=RS
⇒2x-7=5x-61
⇒-7+61=5x-2x
⇒54=3x
⇒x=18
Thus, the measure of QR=2(18)-7=29,RS=5(18)-61=29 and QS=11+18=29.
