Design the rational function with the characteristics: Three real zeros, one of multiplicity 2 ; y − intercept 1 ; vertical asymptotes x = − 2 and x = 3 ; oblique asymptote y = 2 x + 1 . Is this rational function unique?
Design the rational function with the characteristics: Three real zeros, one of multiplicity 2 ; y − intercept 1 ; vertical asymptotes x = − 2 and x = 3 ; oblique asymptote y = 2 x + 1 . Is this rational function unique?
Design the rational function with the characteristics:
Three real zeros, one of multiplicity 2 ; y− intercept 1 ; vertical asymptotes x=−2 and x=3 ; oblique asymptote y=2x+1 . Is this rational function unique?
Expert Solution & Answer
Answer to Problem 90RE
The function is f(x)=2(x−2)(x−3/2)(x−1)(x+2)(x+3) and the rational function is not unique.
Explanation of Solution
Given:
Three real zeros, one of multiplicity 2 ; y− intercept 1 ; vertical asymptotes x=−2 and x=3 ; oblique asymptote y=2x+1 .
Concept Used:
Rational Function
f(x)=axn+....bxm+...
Where n is largest exponent in numerator and m is the largest exponent in denominator.
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