Rational Functions

Question 1

What is the domain of a rational function?

Answer 1

All real numbers excluding those that result in the denominator being equal to zero

Question 2

How do you find the range of a rational function?

Answer 2

Make x the subject and find the values of y for which the function is valid

Question 3

What are the three cases under under which we can have horizontal asymptotes

Answer 3

If the degree of the numerator is greater than the denominator, divide the functions by each other. The quotient is the asymptote

If the degree of the numerator is less than the denominator, the asymptote is y=0

If the degree of the numerator is equal to the denominator, the asymptote is found by dividing the coefficients of x with the highest degree

Question 4

How do you find the vertical asymptote?

Answer 4

Find the values of x for which the denominator is equal to zero

Question 5

What else do you need to sketch a rational function?

Answer 5

x and y inercepts, behaviour as x approaches asymptotes from positve and negative sides, stationary points.