Rational
Functions
Understanding the relationship between rational functions and their reciprocals
Reciprocal Functions (graphing)
Quotients of Polynomial Functions (finding holes, asymptotes, and their equations)
Key Points:
Key Points:
Reciprocal y-coordinates of the original function are the y-coordinates of the reciprocal
X-coordinates of the zeroes of the original function are the locations of the vertical asymptotes of the reciprocal
If the original function is linear or quadratic, x=0 will always be the horizontal asymptote of the reciprocal
The reciprocal and the original have the same negative and positive values
The reciprocal and the original have opposite increasing/decreasing values
Holes are created when a common factor occurs in both the numerator and denominator
Vertical asymptotes occur at the values of “x” that make the denominator = 0
Horizontal asymptotes occur when degree of numerator is less than degree of denominator
Divide leading coefficients to find equation ( y = ___ )
Oblique asymptotes occur when degree of numerator is one greater than degree of denominator
Divide numerator by denominator to find equation of oblique asymptote (ignore remainder)