Graphing Rational Functions
Graph the following rational function and answer the following questions.
Compare the degree of the numerator (n) and the degree of the denominator (d).
If n < d, then H.A. at y = 0
If n = d, then H.A. at y = (lead coefficient/lead coefficient)
If n > d, then there is a slant asymptote
so the H.A. for f(x) is at y = 1.
Occur when a number makes the denominator equal 0. These numbers would make the fraction undefined.
so the V.A. for f(x) is at x = -2.
Any number that make the numerator equal 0 is an x-intercept.
Y-intercepts occur at the result from plugging zero in for x.
Domain - All the possible x-values that can be used in the function.
Range - All possible results from the inputs.
Find the DOMAIN and RANGE for:
Begin with the graph for the function.
In this graph, any number could be x (domain), except -2.
-2 makes the denominator zero, so it is not permitted.
Domain: All real numbers except -2
For the range, this graph shows our results could be any value except 1.
Range: All real numbers except 1