ASAP, pls I need help with these questions
1 answer:
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Answer:
<em>x=8</em>
Step-by-step explanation:
<u>Discontinuity of a Function</u>
We can find some functions whose graphs cannot be plotted in one stroke. It can be a hole or a vertical asymptote or a jump. To find a possible hole in a rational function, we must set both numerator and denominator to 0 independently. If a common point is found, it's a candidate for a hole if the function could eventually be redefined as continuous.
Let's find the zeros of the numerator
Factoring
We find two solutions: x=0, x=8
Let's find the zeros of the denominator
Factoring
We find three roots: x=0, x=8, x=-8
There are two common points where the function can have holes, those are
We are not sure if those values are holes or not until we find the limits
Simplifying
Since the limit exists, the function can be redefined to cover up the hole. Now let's find the limit in x=0
Simplifying
The limit does not exist and goes to infinity, it's not a hole, thus the only hole occurs when x=8