Rtionl Prents (pp of 4) Unit: 08 Lesson: 0 The grphs below describe two prent functions, ech of which is referred to s rtionl function Why do you think they re clled rtionl functions? From the grphs, provide the requested informtion bout ech function f ( ) f ( ) Domin: Rnge: Verticl Asymptote: Horizontl Asymptote: Domin: Rnge: Verticl Asymptote: Horizontl Asymptote: In the sections tht follow, nswer questions bout trnsformtions of ech rtionl prent function ) The figure shows f ( ) On the sme grid, sketch nd lbel the grphs of the functions listed below ) The figure shows f ( ) On the sme grid, sketch nd lbel the grphs of the functions listed below A) 3 3 f ( ) C) f ( ) 3 A) f ( ) C) f ( ) 3 B) 6 6 f ( ) D) f ( ) B) f ( ) D) f ( ) 3) Discuss the ffects of the vlue on the grphs of functions of the form f ( ) or f ( ) 009, TESCCC 04/03/0
Rtionl Prents (pp of 4) Unit: 08 Lesson: 0 The functions below re trnsformtions of the rtionl prent functions, f ( ) nd f ( ) Grph ech in window [-575, 6] by [-5, 5], nd tell the loctions of the verticl symptotes (VA) nd horizontl symptotes (HA) 4) f ( ) 5) f ( ) 6) f ( ) VA: VA: VA: HA: HA: HA: 7) ( ) f 3 8) f ( ) 9) f ( ) 3 ( 3) ( 3) VA: VA: VA: HA: HA: HA: 0) Discuss how vlues of h nd k ffect the grphs of f ( ) k nd f h ( ) ( h) k 009, TESCCC 04/03/0
Rtionl Prents (pp 3 of 4) Unit: 08 Lesson: 0 ) Without the id of clcultor, sketch the grph of ech trnsformtion of f ( ) ) Without the id of clcultor, sketch the grph of ech trnsformtion of f ( ) A) f ( ) A) f ( ) 5 6 ( 4) B) f( ) 4 5 B) f ( ) 4 ( 3) 9 8 C) f ( ) C) f ( ) 6 3 ( ) 009, TESCCC 04/03/0
Rtionl Prents (pp 4 of 4) Unit: 08 Lesson: 0 Write functions of the form f ( ) k or f ( ) k to mtch the grphs below h ( h) Here, ssume tht vlues of re either or - 3) f () 4) f () 5) f () 6) f () 7) f () 8) f () 009, TESCCC 04/03/0
Rtionl Prents (pp of 4) KEY Unit: 08 Lesson: 0 The grphs below describe two prent functions, ech of which is referred to s rtionl function Why do you think they re clled rtionl functions? Ech is written s frction (or rtio), with numertor nd denomintor From the grphs, provide the requested informtion bout ech function f ( ) f ( ) Domin: (, 0) (0, ) Domin: (, 0) (0, ) Rnge: (, 0) (0, ) Rnge: (0, ) Verticl Asymptote: = 0 Verticl Asymptote: = 0 Horizontl Asymptote: y = 0 Horizontl Asymptote: y = 0 In the sections tht follow, nswer questions bout trnsformtions of ech rtionl prent function ) The figure shows f ( ) On the sme grid, sketch nd lbel the grphs of the functions listed below ) The figure shows f ( ) On the sme grid, sketch nd lbel the grphs of the functions listed below A) 3 3 f ( ) C) f ( ) 3 A) f ( ) C) f ( ) 3 B) 6 6 f ( ) D) f ( ) B) f ( ) D) f ( ) 3) Discuss the ffects of the vlue on the grphs of functions of the form f ( ) or f ( ) The -vlue stretches the grph verticlly when >, nd compresses it when 0 < < If is negtive (or, < 0), then the grph is reflected over the -is 009, TESCCC 04/03/0
Rtionl Prents (pp of 4) KEY Unit: 08 Lesson: 0 The functions below re trnsformtions of the rtionl prent functions, f ( ) nd f ( ) Grph ech in window [-575, 6] by [-5, 5], nd tell the loctions of the verticl symptotes (VA) nd horizontl symptotes (HA) 4) f ( ) 5) f ( ) 6) f ( ) VA: = 0 VA: = - VA: = - HA: y = HA: y = 0 HA: y = 7) ( ) f 3 8) f ( ) 9) f ( ) 3 ( 3) ( 3) VA: = 0 VA: = 3 VA: = 3 HA: y = -3 HA: y = 0 HA: y = -3 0) Discuss how vlues of h nd k ffect the grphs of f ( ) k nd f h ( ) ( h) k Vlues of h trnslte the grph to the right (h > 0) or left (h < 0) Vlues of k trnslte the grph up (k > 0) or down (k < 0) For functions of one of these forms, the verticl symptote will be t = h, nd the horizontl symptote will be t y = k 009, TESCCC 04/03/0
Rtionl Prents (pp 3 of 4) KEY Unit: 08 Lesson: 0 ) Without the id of clcultor, sketch the grph of ech trnsformtion of f ( ) ) Without the id of clcultor, sketch the grph of ech trnsformtion of f ( ) A) f ( ) A) f ( ) 5 6 ( 4) B) f( ) 4 5 B) f ( ) 4 ( 3) 9 8 C) f ( ) C) f ( ) 6 3 ( ) The dotted function shows = (not = 9) The dotted function shows = (not = 8) 009, TESCCC 04/03/0
Rtionl Prents (pp 4 of 4) KEY Unit: 08 Lesson: 0 Write functions of the form f ( ) k or f ( ) k to mtch the grphs below h ( h) Here, ssume tht vlues of re either or - 3) f () 4 4) f () 3 5 5) () ( 7) f 6) f () 3 7) () ( 3) f 4 8) () ( 4) f 009, TESCCC 04/03/0