SOLUTION: Consider the function f(x)=2+1/(x-1) 1. Rewrite this function as a single fraction over the denominator i. 2. Find the domain of this hyperbola 3. Explain, in complete se

Algebra ->  Rational-functions -> SOLUTION: Consider the function f(x)=2+1/(x-1) 1. Rewrite this function as a single fraction over the denominator i. 2. Find the domain of this hyperbola 3. Explain, in complete se      Log On


   

Question 1194757: Consider the function f(x)=2+1/(x-1)
1. Rewrite this function as a single fraction over the denominator i.
2. Find the domain of this hyperbola
3. Explain, in complete sentences, how you use this information to determine the vertical asymptote for this function. Then write the equation of the vertical asymptote.
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Consider the function f%28x%29=2%2B1%2F%28x-1%29
1. Rewrite this function as a single fraction over the denominator i.
f%28x%29=2%2B1%2F%28x-1%29
f%28x%29=%282%28x-1%29%29%2F%28x-1%29%2B1%2F%28x-1%29
f%28x%29=%282x-2%29%2F%28x-1%29%2B1%2F%28x-1%29
f%28x%29=%282x-2%2B1%29%2F%28x-1%29
f%28x%29=%282x-1%29%2F%28x-1%29


2. Find the domain of this hyperbola

domain: all x except that makes denominator equal to zero
that is %28x-1%29=0 => x=1
so, domain is: { x element R : x%3C%3E1 }

3. Explain, in complete sentences, how you use this information to determine the vertical asymptote for this function. Then write the equation of the vertical asymptote.
For rational functions, the vertical asymptotes are the undefined points, also known as the zeros of the denominator, of the simplified function. So, in your case, the vertical asymptote is x=1.