Rational Functions

Question 1

What is a Rational Functions?

Answer 1

A function whose rule can be written as the ratio of two polynomials.

Question 2

What are the characteristics for a rational function of the form f(x)=(a/(x-h))+k?

Answer 2

The graph is a hyperbola, there is a vertical asymptote at the lines x=h, the domain is x doesn’t equal h, and there is a horizontal asymptote at the line y=k with the range y doesn’t equal k.

Question 3

What are the characteristics for a rational function of the form f(x)=((p(x)/q(x))?

Answer 3

If the function has no common factors other than 1, the graph can only have up to one horizontal asymptote. If the degree of p is less than the degree of q, the horizontal asymptote is y=0. If the degree of p is greater than the degree of q, then there is no horizontal asymptote. If the degree of p equals the degree of q, the horizontal asymptote is the line y=leading coefficient of p/leading coefficient of q.

If the function has no common factors other than 1, the function f has zeros at each real value for x for which p(x)=0. A vertical asymptote at each real value of x for which q(x)=0.

Question 4

What is a Hole?

Answer 4

An omitted point in a graph.