Write (8a^-6) in simplest form.
1 answer:
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Recall that a rational function:
has a vertical asymptote at x₀ if and only if:
Also, the roots of the above rational function are the same as P(x).
Since the rational function has a vertical asymptote at x=-1, we get that its denominator must be:
Since the rational function has a double zero at x=2 we get that its numerator must be of the form:
Finally, since the rational function has y-intercept at (0,2) we get that:
Simplifying the above equation we get:
Dividing the above equation by 4 we get:
Therefore, the rational function that satisfies the given conditions is:
Answer:
The numerator is:
The denominator is:
We have the expression:
When we have rational functions, where the denominator is a function of x, we have a restriction for the domain for any value of x that makes the denominator equal to 0.
That is because if the denominator is 0, then we have a function f(x) that is a division by zero and is undefined.
If we have a value that makes f(x) to be undefined, then this value of x does not belong to the domain of f(x).
Expression:
Answer: There is no restriction for x in the expression.