Factor completely x8 − 81.
2 answers:
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Answer:
We have the functions,
and
.
After plotting both the functions, we see that,
The graph of F(x) is given below, which has the y-intercept at (0,-1.5) and its horizontal asymptote is x-axis.
Also, the graph of f(x) is a straight line passing through (-4,0) and (0,2).
Further, we can see that the two graphs have intersection points as (-4.873,-0.436) and (2.873,3.436).
Given vertical asymptotes x = 2 and x = -5 .
Therefore Factors of denominator (x-2)(x+5).
x-intercepts (-1,0) and (1,0) .
Therefore factors of (x+1)(x-1).
So far we got rational function = .
Now, we are given horizontal asymptote at y = 9.
Multiplying above express by 9 on the top, we get
.