Function and the Graph

Rational Functions Function and the graph Real Roots: Set the Discontinuities***: Factor the Domain: x ≠ Horizontal Asymptotes: numerator equal to zero denominator then set factors equal discontinuities BOBO f(x) = x n + x n-1 + … + a and solve for x. to zero and solve. BOTN xm +xm-1 + … + b EATS DC x  3 f(x) = x 2  x  6

x 1 f(x) = x  4

x 2  3x  2 f(x) = x  5

***Discontinuities: Factors that cancel give HOLES and factors that do not cancel give vertical ASYMPTOTES. Holes are considered removable d iscontinuities, while asymptotes are nonremovable. Rational Functions Function and the graph Real Roots: Set the Discontinuities***: Factor the Domain: x ≠ Horizontal Asymptotes: numerator equal to zero denominator then set factors equal discontinuities BOBO f(x) = x n + x n-1 + … + a and solve for x. to zero and solve. . BOTN xm +xm-1 + … + b EATS DC 3x  6 f(x) = x 2  4

x  3 f(x) = x 2  8

x 2  5x f(x) = x  2

***Discontinuities: Factors that cancel give HOLES and factors that do not cancel give vertical ASYMPTOTES. Holes are considered removable d iscontinuities, while asymptotes are nonremovable.