Answer:
As x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function .
Therefore, x = -5, x = 2 and y = 3 is the right option.
Step-by-step explanation:
As the given function is
<u><em>Determining Vertical Asymptote:</em></u>
The line x = L is a vertical asymptote of the function if if the limit of the function (one-sided) at this point is infinite.
In other words, it means that possible points are points where the denominator equals 0 or doesn't exist.
Such as
x=−5 , check:
Since, the limit is infinite, then <em>x = -5</em> is a <em>vertical asymptote</em>.
x = 2, check:
Since the limit is infinite, then <em>x = 2</em> is a <em>vertical asymptote</em>.
<u><em>Determining Horizontal Asymptote:</em></u>
Line y=L is a horizontal asymptote of the function y = f(x), if either
or and L is finite.
<em>Calculating the limits:</em>
<em></em>
<em></em>
<em>Thus, the </em><em>horizontal asymptote</em><em> is </em><em>y=3.</em>
So, x = -5, x = 2 and y = 3 are the equations of the asymptotes of the graph of the function .
Therefore, x = -5, x = 2 and y = 3 is the right option.
<em>Keywords: asymptote, vertical asymptote, horizontal asymptote, equation</em>
<em>Learn more about asymptotes from brainly.com/question/11268104</em>
<em>#learnwithBrainly</em>