Kuta Software - Infinite Algebra 2 Name___________________________________ Graphing Rational Functions Date________________ Period____ Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of each. 1) f ( x) = x x 2) f ( x) = x x 3) f ( x) = x x x x x 4) f ( x) = x x x x Identify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then sketch the graph. 5) f ( x) = x x 6) f ( x) = x x y x x x 8) f ( x) = x x x x y x x 7) f ( x) = y x ©3 M2H011n2G tKfu7tUaM jSZoafStgwza4rGe8 4L9LWCo.o w mAblXlS 5rMi4gQhUthsa VrReas3e2revreBdU.a P BMBahdAeH iw2iJtLhf lI9nJfciZnXiVtJeX qABlRgme4bXrsaM k2K.w -1- y Worksheet by Kuta Software LLC x x 9) f ( x) = x x x x 10) f ( x) = x x y x 12) f ( x) = y x y x ©n E2O0B1b2T 4Kyu7tlaO US9o5fVtvwyaXrneb 3LWLhCL.N 7 VAWlhlB erMiNgzhktXsr VrheRsYemrJv1eHdJ.z t jMRakd7ea zwJiftwhY gIOnifzidnOiDtUel zAplegMeXburoaT J2f.u -2- x x x x y 14) f ( x) = x x x x 13) f ( x) = x x x x 11) f ( x) = x y y Worksheet by Kuta Software LLC Kuta Software - Infinite Algebra 2 Name___________________________________ Graphing Rational Functions Date________________ Period____ Identify the points of discontinuity, holes, vertical asymptotes, x-intercepts, and horizontal asymptote of each. x x x Discontinuities: , 2) f ( x) = Discontinuities: x Vertical Asym.: x, x Vertical Asym.: x Holes: None Holes: None Horz. Asym.: y Horz. Asym.: y X-intercepts: None X-intercepts: x x x x x 3) f ( x) = Discontinuities: , 4) f ( x) = Discontinuities: , x x Vertical Asym.: x, x x x Vertical Asym.: x 1) f ( x) = Holes: None Horz. Asym.: None X-intercepts: , , Holes: x Horz. Asym.: y X-intercepts: Identify the points of discontinuity, holes, vertical asymptotes, and horizontal asymptote of each. Then sketch the graph. 5) f ( x) = x x 6) f ( x) = y Discontinuities: , Vertical Asym.: x, x Holes: None Horz. Asym.: y x x x 8) f ( x) = y x x x x y Discontinuities: , Vertical Asym.: x Holes: x Horz. Asym.: None x Discontinuities: Vertical Asym.: x Holes: None Horz. Asym.: y x x 7) f ( x) = Discontinuities: Vertical Asym.: x Holes: None Horz. Asym.: y y x ©0 E2i0E1S2v xKJultdam GSOovfItKwJa2reeR hLXLLC4.p W tA0lelK jrvitgRh2tOs9 mrEeZsoeUrGvLead0.H n MMLaRdce6 awliptphJ jIbnlfmiCn4i8tje7 NA3lkgOeFb4rWan e2Z.q -1- x Worksheet by Kuta Software LLC x x 9) f ( x) = x x x x 10) f ( x) = x x y Discontinuities: , Vertical Asym.: x, x Holes: None Horz. Asym.: y x 12) f ( x) = y Discontinuities: Vertical Asym.: x Holes: None Horz. Asym.: None x 14) f ( x) = x y Discontinuities: Vertical Asym.: x Holes: None Horz. Asym.: y x Discontinuities: , Vertical Asym.: x Holes: x Horz. Asym.: y Discontinuities: Vertical Asym.: x Holes: None Horz. Asym.: y x y y x x Discontinuities: , Vertical Asym.: x, x Holes: None Horz. Asym.: None x x 13) f ( x) = x x y x x 11) f ( x) = x x x Create your own worksheets like this one with Infinite Algebra 2. Free trial available at KutaSoftware.com ©6 m2F0y1T23 wKoujtUan zSVonfxtqwfaJrwex DLuL1Cz.x N XAclQlu 5rRi5gmh8tRsC urielsAesrTvweHdv.E U rMJazdke9 dwFiotCh6 wIVnufriYnzi8tGei WAUlDgmekbmr6aO 022.W -2- Worksheet by Kuta Software LLC