1.

Write a rational function g with vertical asymptotes at x = 3 and x = -3, a horizontal asymptote at y = -4 and with no x-intercept.

Answer»

Solution :`*` Since g has vertical is asymptotes x = 3 and x = -3, then the denominatorof the rational function contains theproduct of (x-3) and (x+3) . Function g has the form
`g(x)=(H(x))/((x-3)(x+3)`
`*` For the horizontal asymptote to EXIST, the numerator h(x) of g(x) has same DEGREE as that of the denominator with a leading COEFFICIENT equal to -4. At the same time, h(x) has no REAL zeros. Hence
`f(x)=(-4x^(2)-6)/((x-3)(x+3))`
`*` Check the characteristics in the graph of g shown below.


Discussion

No Comment Found

Related InterviewSolutions