SOLUTION: Write the equation of a possible rational function given the following information. Leave in factored form. Vertical asymptote x = 2, discontinuous point (−3, −4/5), x - int

Algebra ->  Rational-functions -> SOLUTION: Write the equation of a possible rational function given the following information. Leave in factored form. Vertical asymptote x = 2, discontinuous point (−3, −4/5), x - int      Log On


   

Question 1206908: Write the equation of a possible rational function given the following information. Leave in factored form.
Vertical asymptote x = 2, discontinuous point (−3, −4/5), x - intercept at x = −5 and horizontal asymptote at y = 2.
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
a rational function :
R%28x%29+=+a%2Ap%28x%29+%2Fq%28x%29+
where p%28x%29 and q%28x%29 are both polynomials
given:
Vertical asymptote x+=+2: value of x that makes denominator equal to zero , so
q%28x%29=%28x-2%29

x - intercept at x+=+-5=>numerator is
p%28x%29=a%28x%2B5%29

so far R%28x%29=a%28x%2B5%29%2F%28x-2%29

horizontal asymptote at y=2, the highest power of numerator and denominator are same and coefficient of numerator is a=2 times that of denominator

R%28x%29=2%28x%2B5%29%2F%28x-2%29

discontinuous point (-3, -4%2F5)

check given point
-4%2F5=2%28-3%2B5%29%2F%28-3-2%29=> true

=>for x=-3, denominator will be zero, so add %28x%2B3%29 to both, numerator and denominator, and your equation is:

R%28x%29+=+2%28%28x%2B5%29%28x%2B3%29%29%2F%28%28x-2%29%28x%2B3%29%29