Rational Functions and Graphs

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functions with an x in the denominator (_/x) and/or numerator are known as RATIONAL FUNCTIONS.

the parent function is y=1/x.

in the parent function, x cannot equal 0. y cannot equal 0 either.

the graphs of rational functions have TWO ASYMPTOTES (one horizontal & one vertical).

f(x) = a/(x-h) +k

parent function DOMAIN: (-infinity, 0) U (0, infinity)

parent function RANGE: (-infinity, 0) U (0, infinity)

graphical discontinuities

a point of discontinuity is an x-value that makes the denominator 0. to find a point of discontinuity, you set the denominator equal to zero and solve.

hint: FACTOR

points of discontinuity can be one of two different types:

1) a removable discontinuity (hole) - factors cancel out.

2) a vertical asymptote - factor doesn't cancel out.

a root is where the function crosses the x-axis.

hint: find points of discontinuity before deciding which kind they are.