Belinda keeps a record of her expenses for the week as shown: Bus fare $8.70 Lunch out $7.35 Hair cut $16 Movie rental $5.95 Wha
2 answers:
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a) The polynomial in expanded form is .
b) The slant asymptote is represented by the linear function is .
c) There is a discontinuity at with a slant asymptote.
a) In this question we are going to use the Factor Theorem, which establishes that polynomial are the result of products of binomials of the form , where
is the i-th root of the polynomial and the grade is equal to the quantity of roots. Therefore, the polynomial
has the following form:
And the expanded form is obtained by some algebraic handling:
(1)
The polynomial in expanded form is .
b) In this question we divide the polynomial found in a) (in factor form) by the polynomial (also in factor form). That is:
(2)
The slant asymptote is defined by linear function, whose slope () and intercept (
) are determined by the following expressions:
(3)
(4)
If , then the equation of the slant asymptote is:
The slant asymptote is represented by the linear function is .
c) The number of discontinuities in rational functions is equal to the number of binomials in the denominator, which was determined in b). Hence, we have a discontinuity at with a slant asymptote.
We kindly invite to check this question on asymptotes: brainly.com/question/4084552
