Question

Write the equation of a rational function f(x) = p(×)/q(x) having the indicated properties, in which the degrees of p and q are as small as possible. More than one correct function may be possible. Graph your function using a graphing utility to verify that it has the required properties.

134.) f has a vertical asymptote given by x=3, a horizontal asymptote y=0, y-intercept at -1, and no x-intercept

135.) f has vertical asymptotes given by x=-2 and x=2, a horizontal asymptote y=2, intercept at 9/2, x-intercepts at -3 and 3, and y-axis symmetry

Please helppp, thank youu​

Answer 1

134. y = 3 / (x-3) attachment picture 1

135. y = (2*(x+3)(x-3)) / (x+2)(x-2) attachment picture 2

Explanation:

134. y = 3¹ / (x¹-3)

135. y = (2*(x+3)(x-3)) / (x+2)(x-2)

Apply the asymptote properties to verify, such as compare the degree of numerator and denominator... denominator approach 0 etc.