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FIU / Mathematics: Calculus and Precalculus / MAC 1140 / Define leading coefficient test.

Define leading coefficient test.

Define leading coefficient test.

Description

School: Florida International University
Department: Mathematics: Calculus and Precalculus
Course: PreCalculus Algebra
Term: Fall 2018
Tags: polynomials
Cost: 50
Name: MAC1140 Chapter 3 Exam Study Guide
Description: These notes cover what will be on our exam 10/02.
Uploaded: 09/12/2018
2 Pages 113 Views 1 Unlocks
Reviews

geral_p14 (Rating: )

There is info missing on section 3.6



.lst-kix_2ubg9nge73ux-8 > li:before{content:"■ "}.lst-kix_2ubg9nge73ux-5 > li:before{content:"■ "}.lst-kix_2ubg9nge73ux-4 > li:before{content:"○ "}.lst-kix_2ubg9nge73ux-3 > li:before{content:"● "}ol.lst-kix_bvavcgbwe4f6-2.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-2 0}.lst-kix_2ubg9nge73ux-6 > li:before{content:"● "}.lst-kix_bvavcgbwe4f6-2 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-2}.lst-kix_2ubg9nge73ux-7 > li:before{content:"○ "}.lst-kix_8epmcxew9irf-1 > li:before{content:"○ "}.lst-kix_8epmcxew9irf-3 > li:before{content:"● "}.lst-kix_8epmcxew9irf-0 > li:before{content:"● "}.lst-kix_8epmcxew9irf-4 > li:before{content:"○ "}ol.lst-kix_h6c3a4rs5nxa-3.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-3 0}.lst-kix_8epmcxew9irf-2 > li:before{content:"■ "}.lst-kix_5i734vn3sen-5 > li:before{content:"■ "}.lst-kix_5i734vn3sen-4 > li:before{content:"○ "}.lst-kix_5i734vn3sen-6 > li:before{content:"● "}.lst-kix_2ubg9nge73ux-0 > li:before{content:"● "}.lst-kix_2ubg9nge73ux-2 > li:before{content:"■ "}.lst-kix_2ubg9nge73ux-1 > li:before{content:"○ "}.lst-kix_8epmcxew9irf-8 > li:before{content:"■ "}.lst-kix_5i734vn3sen-8 > li:before{content:"■ "}.lst-kix_8epmcxew9irf-5 > li:before{content:"■ "}.lst-kix_8epmcxew9irf-7 > li:before{content:"○ "}.lst-kix_5i734vn3sen-7 > li:before{content:"○ "}.lst-kix_8epmcxew9irf-6 > li:before{content:"● "}.lst-kix_bvavcgbwe4f6-4 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-4}.lst-kix_5i734vn3sen-1 > li:before{content:"○ "}.lst-kix_5i734vn3sen-2 > li:before{content:"■ "}.lst-kix_5i734vn3sen-3 > li:before{content:"● "}.lst-kix_5i734vn3sen-0 > li:before{content:"➢ "}.lst-kix_h6c3a4rs5nxa-5 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-5}ol.lst-kix_h6c3a4rs5nxa-8.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-8 0}.lst-kix_7ltq8j8n5p0n-0 > li:before{content:"● "}.lst-kix_7ltq8j8n5p0n-2 > li:before{content:"■ "}.lst-kix_b2v65pzfjfmd-4 > li:before{content:"○ "}.lst-kix_b2v65pzfjfmd-6 > li:before{content:"● "}.lst-kix_b2v65pzfjfmd-8 > li:before{content:"■ "}ul.lst-kix_b2v65pzfjfmd-0{list-style-type:none}.lst-kix_7ltq8j8n5p0n-4 > li:before{content:"○ "}ul.lst-kix_b2v65pzfjfmd-1{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-2.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-2 0}.lst-kix_kioaf1c43l2-7 > li:before{content:"○ "}.lst-kix_b2v65pzfjfmd-0 > li:before{content:"● "}.lst-kix_b2v65pzfjfmd-2 > li:before{content:"■ "}ul.lst-kix_b2v65pzfjfmd-2{list-style-type:none}ul.lst-kix_b2v65pzfjfmd-3{list-style-type:none}ul.lst-kix_b2v65pzfjfmd-4{list-style-type:none}ul.lst-kix_b2v65pzfjfmd-5{list-style-type:none}ul.lst-kix_b2v65pzfjfmd-6{list-style-type:none}ul.lst-kix_b2v65pzfjfmd-7{list-style-type:none}ul.lst-kix_2ubg9nge73ux-0{list-style-type:none}.lst-kix_7ltq8j8n5p0n-8 > li:before{content:"■ "}ul.lst-kix_b2v65pzfjfmd-8{list-style-type:none}ul.lst-kix_2ubg9nge73ux-2{list-style-type:none}.lst-kix_kioaf1c43l2-3 > li:before{content:"● "}.lst-kix_kioaf1c43l2-5 > li:before{content:"■ "}ul.lst-kix_2ubg9nge73ux-1{list-style-type:none}ul.lst-kix_hxpgofoyn7c3-8{list-style-type:none}ul.lst-kix_2ubg9nge73ux-4{list-style-type:none}ul.lst-kix_2ubg9nge73ux-3{list-style-type:none}.lst-kix_bvavcgbwe4f6-8 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-8}ul.lst-kix_2ubg9nge73ux-6{list-style-type:none}ul.lst-kix_2ubg9nge73ux-5{list-style-type:none}ul.lst-kix_hxpgofoyn7c3-4{list-style-type:none}ul.lst-kix_hxpgofoyn7c3-5{list-style-type:none}ul.lst-kix_hxpgofoyn7c3-6{list-style-type:none}.lst-kix_kioaf1c43l2-1 > li:before{content:"○ "}ul.lst-kix_hxpgofoyn7c3-7{list-style-type:none}ul.lst-kix_hxpgofoyn7c3-0{list-style-type:none}.lst-kix_7ltq8j8n5p0n-6 > li:before{content:"● "}ul.lst-kix_hxpgofoyn7c3-1{list-style-type:none}ul.lst-kix_hxpgofoyn7c3-2{list-style-type:none}.lst-kix_h6c3a4rs5nxa-2 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-2}ul.lst-kix_hxpgofoyn7c3-3{list-style-type:none}.lst-kix_h6c3a4rs5nxa-2 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-2,lower-roman) ". "}.lst-kix_bvavcgbwe4f6-5 > li:before{content:"(" counter(lst-ctn-kix_bvavcgbwe4f6-5,lower-roman) ") "}.lst-kix_bvavcgbwe4f6-7 > li:before{content:"" counter(lst-ctn-kix_bvavcgbwe4f6-7,lower-latin) ". "}.lst-kix_h6c3a4rs5nxa-0 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-0,decimal) ". "}.lst-kix_h6c3a4rs5nxa-4 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-4,lower-latin) ". "}.lst-kix_veaj0mjky95o-1 > li:before{content:"○ "}ul.lst-kix_2ubg9nge73ux-8{list-style-type:none}.lst-kix_veaj0mjky95o-3 > li:before{content:"● "}ul.lst-kix_2ubg9nge73ux-7{list-style-type:none}.lst-kix_veaj0mjky95o-7 > li:before{content:"○ "}.lst-kix_h6c3a4rs5nxa-0 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-0}.lst-kix_geeka5oq5eh7-8 > li:before{content:"■ "}ol.lst-kix_bvavcgbwe4f6-0.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-0 0}.lst-kix_veaj0mjky95o-5 > li:before{content:"■ "}.lst-kix_h6c3a4rs5nxa-8 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-8,lower-roman) ". "}.lst-kix_h6c3a4rs5nxa-6 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-6,decimal) ". "}.lst-kix_bvavcgbwe4f6-1 > li:before{content:"" counter(lst-ctn-kix_bvavcgbwe4f6-1,lower-latin) ") "}.lst-kix_bvavcgbwe4f6-3 > li:before{content:"(" counter(lst-ctn-kix_bvavcgbwe4f6-3,decimal) ") "}ol.lst-kix_bvavcgbwe4f6-3.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-3 0}.lst-kix_nz40ed4sye25-8 > li:before{content:"■ "}.lst-kix_nz40ed4sye25-6 > li:before{content:"● "}ol.lst-kix_h6c3a4rs5nxa-1{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-2{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-0{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-4.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-4 0}ol.lst-kix_h6c3a4rs5nxa-5{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-6{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-3{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-4{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-7{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-8{list-style-type:none}.lst-kix_bvavcgbwe4f6-3 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-3}.lst-kix_h6c3a4rs5nxa-1 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-1}ol.lst-kix_bvavcgbwe4f6-1.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-1 0}.lst-kix_nz40ed4sye25-2 > li:before{content:"■ "}.lst-kix_nz40ed4sye25-0 > li:before{content:"● "}.lst-kix_nz40ed4sye25-4 > li:before{content:"○ "}.lst-kix_h6c3a4rs5nxa-7 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-7}ol.lst-kix_h6c3a4rs5nxa-5.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-5 0}.lst-kix_gn6rwfgiqke7-3 > li:before{content:"● "}.lst-kix_gn6rwfgiqke7-4 > li:before{content:"○ "}.lst-kix_bvavcgbwe4f6-1 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-1}.lst-kix_h6c3a4rs5nxa-8 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-8}.lst-kix_gn6rwfgiqke7-7 > li:before{content:"○ "}.lst-kix_hxpgofoyn7c3-0 > li:before{content:"● "}.lst-kix_gn6rwfgiqke7-5 > li:before{content:"■ "}.lst-kix_gn6rwfgiqke7-6 > li:before{content:"● "}ul.lst-kix_8epmcxew9irf-2{list-style-type:none}ul.lst-kix_8epmcxew9irf-3{list-style-type:none}ul.lst-kix_8epmcxew9irf-0{list-style-type:none}ul.lst-kix_8epmcxew9irf-1{list-style-type:none}.lst-kix_gn6rwfgiqke7-0 > li:before{content:"● "}ul.lst-kix_8epmcxew9irf-8{list-style-type:none}ul.lst-kix_8epmcxew9irf-6{list-style-type:none}.lst-kix_gn6rwfgiqke7-1 > li:before{content:"○ "}.lst-kix_gn6rwfgiqke7-2 > li:before{content:"■ "}ul.lst-kix_8epmcxew9irf-7{list-style-type:none}ul.lst-kix_8epmcxew9irf-4{list-style-type:none}ul.lst-kix_8epmcxew9irf-5{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-6.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-6 0}ul.lst-kix_gn6rwfgiqke7-8{list-style-type:none}ul.lst-kix_gn6rwfgiqke7-7{list-style-type:none}ul.lst-kix_gn6rwfgiqke7-6{list-style-type:none}ul.lst-kix_gn6rwfgiqke7-5{list-style-type:none}ul.lst-kix_gn6rwfgiqke7-4{list-style-type:none}ul.lst-kix_gn6rwfgiqke7-3{list-style-type:none}ul.lst-kix_gn6rwfgiqke7-2{list-style-type:none}.lst-kix_h6c3a4rs5nxa-6 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-6}ul.lst-kix_gn6rwfgiqke7-1{list-style-type:none}.lst-kix_gn6rwfgiqke7-8 > li:before{content:"■ "}ol.lst-kix_h6c3a4rs5nxa-0.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-0 0}ul.lst-kix_kioaf1c43l2-6{list-style-type:none}ol.lst-kix_h6c3a4rs5nxa-7.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-7 0}ul.lst-kix_kioaf1c43l2-7{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-4.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-4 0}ul.lst-kix_kioaf1c43l2-4{list-style-type:none}ul.lst-kix_kioaf1c43l2-5{list-style-type:none}.lst-kix_geeka5oq5eh7-0 > li:before{content:"● "}ul.lst-kix_kioaf1c43l2-8{list-style-type:none}.lst-kix_geeka5oq5eh7-1 > li:before{content:"○ "}ul.lst-kix_kioaf1c43l2-2{list-style-type:none}ul.lst-kix_kioaf1c43l2-3{list-style-type:none}ul.lst-kix_kioaf1c43l2-0{list-style-type:none}ul.lst-kix_kioaf1c43l2-1{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-8{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-6{list-style-type:none}.lst-kix_geeka5oq5eh7-6 > li:before{content:"● "}ol.lst-kix_bvavcgbwe4f6-7{list-style-type:none}.lst-kix_bvavcgbwe4f6-5 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-5}.lst-kix_geeka5oq5eh7-5 > li:before{content:"■ "}.lst-kix_geeka5oq5eh7-2 > li:before{content:"■ "}.lst-kix_geeka5oq5eh7-4 > li:before{content:"○ "}.lst-kix_geeka5oq5eh7-3 > li:before{content:"● "}ol.lst-kix_h6c3a4rs5nxa-1.start{counter-reset:lst-ctn-kix_h6c3a4rs5nxa-1 0}ol.lst-kix_bvavcgbwe4f6-0{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-1{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-5.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-5 0}.lst-kix_hxpgofoyn7c3-7 > li:before{content:"○ "}ul.lst-kix_veaj0mjky95o-0{list-style-type:none}.lst-kix_hxpgofoyn7c3-8 > li:before{content:"■ "}ol.lst-kix_bvavcgbwe4f6-4{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-5{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-2{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-3{list-style-type:none}.lst-kix_hxpgofoyn7c3-2 > li:before{content:"■ "}ul.lst-kix_veaj0mjky95o-6{list-style-type:none}ul.lst-kix_veaj0mjky95o-5{list-style-type:none}.lst-kix_hxpgofoyn7c3-1 > li:before{content:"○ "}.lst-kix_hxpgofoyn7c3-3 > li:before{content:"● "}ul.lst-kix_veaj0mjky95o-8{list-style-type:none}ul.lst-kix_veaj0mjky95o-7{list-style-type:none}ul.lst-kix_veaj0mjky95o-2{list-style-type:none}ul.lst-kix_veaj0mjky95o-1{list-style-type:none}ul.lst-kix_veaj0mjky95o-4{list-style-type:none}ul.lst-kix_veaj0mjky95o-3{list-style-type:none}.lst-kix_hxpgofoyn7c3-6 > li:before{content:"● "}.lst-kix_hxpgofoyn7c3-5 > li:before{content:"■ "}.lst-kix_hxpgofoyn7c3-4 > li:before{content:"○ "}.lst-kix_7ltq8j8n5p0n-1 > li:before{content:"○ "}.lst-kix_bvavcgbwe4f6-7 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-7}.lst-kix_b2v65pzfjfmd-7 > li:before{content:"○ "}.lst-kix_kioaf1c43l2-8 > li:before{content:"■ "}.lst-kix_b2v65pzfjfmd-3 > li:before{content:"● "}ul.lst-kix_5i734vn3sen-0{list-style-type:none}ul.lst-kix_5i734vn3sen-1{list-style-type:none}ul.lst-kix_5i734vn3sen-2{list-style-type:none}ul.lst-kix_5i734vn3sen-3{list-style-type:none}.lst-kix_7ltq8j8n5p0n-3 > li:before{content:"● "}.lst-kix_kioaf1c43l2-6 > li:before{content:"● "}.lst-kix_b2v65pzfjfmd-1 > li:before{content:"○ "}ul.lst-kix_7ltq8j8n5p0n-5{list-style-type:none}ul.lst-kix_5i734vn3sen-8{list-style-type:none}ul.lst-kix_geeka5oq5eh7-4{list-style-type:none}ul.lst-kix_7ltq8j8n5p0n-4{list-style-type:none}ul.lst-kix_geeka5oq5eh7-5{list-style-type:none}ul.lst-kix_7ltq8j8n5p0n-3{list-style-type:none}ul.lst-kix_geeka5oq5eh7-6{list-style-type:none}ul.lst-kix_7ltq8j8n5p0n-2{list-style-type:none}ul.lst-kix_geeka5oq5eh7-7{list-style-type:none}ul.lst-kix_7ltq8j8n5p0n-1{list-style-type:none}ul.lst-kix_5i734vn3sen-4{list-style-type:none}ul.lst-kix_geeka5oq5eh7-0{list-style-type:none}ul.lst-kix_7ltq8j8n5p0n-0{list-style-type:none}ul.lst-kix_5i734vn3sen-5{list-style-type:none}ul.lst-kix_geeka5oq5eh7-1{list-style-type:none}ul.lst-kix_5i734vn3sen-6{list-style-type:none}ul.lst-kix_geeka5oq5eh7-2{list-style-type:none}ul.lst-kix_5i734vn3sen-7{list-style-type:none}.lst-kix_kioaf1c43l2-0 > li:before{content:"● "}.lst-kix_kioaf1c43l2-4 > li:before{content:"○ "}ul.lst-kix_geeka5oq5eh7-3{list-style-type:none}.lst-kix_7ltq8j8n5p0n-5 > li:before{content:"■ "}.lst-kix_7ltq8j8n5p0n-7 > li:before{content:"○ "}ul.lst-kix_7ltq8j8n5p0n-8{list-style-type:none}ul.lst-kix_7ltq8j8n5p0n-7{list-style-type:none}ul.lst-kix_7ltq8j8n5p0n-6{list-style-type:none}.lst-kix_kioaf1c43l2-2 > li:before{content:"■ "}.lst-kix_veaj0mjky95o-0 > li:before{content:"● "}.lst-kix_h6c3a4rs5nxa-1 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-1,lower-latin) ". "}.lst-kix_h6c3a4rs5nxa-5 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-5,lower-roman) ". "}.lst-kix_bvavcgbwe4f6-4 > li:before{content:"(" counter(lst-ctn-kix_bvavcgbwe4f6-4,lower-latin) ") "}.lst-kix_bvavcgbwe4f6-8 > li:before{content:"" counter(lst-ctn-kix_bvavcgbwe4f6-8,lower-roman) ". "}.lst-kix_veaj0mjky95o-2 > li:before{content:"■ "}.lst-kix_veaj0mjky95o-4 > li:before{content:"○ "}ul.lst-kix_geeka5oq5eh7-8{list-style-type:none}.lst-kix_h6c3a4rs5nxa-3 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-3,decimal) ". "}.lst-kix_bvavcgbwe4f6-6 > li:before{content:"" counter(lst-ctn-kix_bvavcgbwe4f6-6,decimal) ". "}.lst-kix_geeka5oq5eh7-7 > li:before{content:"○ "}.lst-kix_h6c3a4rs5nxa-3 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-3}.lst-kix_veaj0mjky95o-6 > li:before{content:"● "}.lst-kix_veaj0mjky95o-8 > li:before{content:"■ "}ol.lst-kix_bvavcgbwe4f6-6.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-6 0}.lst-kix_bvavcgbwe4f6-0 > li:before{content:"" counter(lst-ctn-kix_bvavcgbwe4f6-0,decimal) ") "}.lst-kix_h6c3a4rs5nxa-7 > li:before{content:"" counter(lst-ctn-kix_h6c3a4rs5nxa-7,lower-latin) ". "}.lst-kix_b2v65pzfjfmd-5 > li:before{content:"■ "}.lst-kix_bvavcgbwe4f6-2 > li:before{content:"" counter(lst-ctn-kix_bvavcgbwe4f6-2,lower-roman) ") "}.lst-kix_nz40ed4sye25-7 > li:before{content:"○ "}ul.lst-kix_gn6rwfgiqke7-0{list-style-type:none}ol.lst-kix_bvavcgbwe4f6-7.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-7 0}ul.lst-kix_nz40ed4sye25-1{list-style-type:none}ul.lst-kix_nz40ed4sye25-0{list-style-type:none}ul.lst-kix_nz40ed4sye25-3{list-style-type:none}ul.lst-kix_nz40ed4sye25-2{list-style-type:none}.lst-kix_h6c3a4rs5nxa-4 > li{counter-increment:lst-ctn-kix_h6c3a4rs5nxa-4}.lst-kix_bvavcgbwe4f6-0 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-0}ul.lst-kix_nz40ed4sye25-8{list-style-type:none}ul.lst-kix_nz40ed4sye25-5{list-style-type:none}ul.lst-kix_nz40ed4sye25-4{list-style-type:none}ul.lst-kix_nz40ed4sye25-7{list-style-type:none}.lst-kix_bvavcgbwe4f6-6 > li{counter-increment:lst-ctn-kix_bvavcgbwe4f6-6}ul.lst-kix_nz40ed4sye25-6{list-style-type:none}.lst-kix_nz40ed4sye25-3 > li:before{content:"● "}.lst-kix_nz40ed4sye25-1 > li:before{content:"○ "}.lst-kix_nz40ed4sye25-5 > li:before{content:"■ "}ol.lst-kix_bvavcgbwe4f6-8.start{counter-reset:lst-ctn-kix_bvavcgbwe4f6-8 0}

MAC 1140 Test 2 Notes If you want to learn more check out What is the gene that is necessary to produce a trait?

> Chapter 3

  • Polynomial function of degree n:

        f(x)=an xn +a  n-1 xn-1 + … +a2x2 + a,x + ao

  • On with the highest power is leading coefficient
  • N is non-negative , and no function.

We also discuss several other topics like What is the spanish of pen?
If you want to learn more check out Who turned odysseus’s crew to pigs?

Leading Coefficiant Test

  • If ‘n’ is odd: 1POSITIVE leading coefficient= it falls left and rises right. 2.Negative leading coefficient= rises left falls right.
  • If ‘n’ is EVEN: 1positive leading coefficient= rises left rises right. 2negative leading coefficient falls left falls right.

We also discuss several other topics like What is teleological fallacy?

Odd n

Even n

an>0

an<0

Don't forget about the age old question of What is an enthymeme?

  • Zeros of polynomial functions.
  • Zeros are roots, solutions, and x-intercepts
  • To find zeros, equal equation to 0.

Don't forget about the age old question of What is the recommended amount of calories per day for humans?

Example: f(x) = - x4 + 4x3 - 4x2

  1. -x4 + 4x3 - 4x2 = 0
  2. X4 - 4x + 4x2 = 0
  3. X4 - 4x + 4x2 = 0
  4. X2 (x-2) 2 = 0
  5. X2 = 0 and x - z = 0       } 0 and 2 are both zeros with multiplicity 2.
  6. X = 0 x = 2

Multiplicity and x-intercepts

  • If the multiplicity of a zero is EVEN, then the graph touches x axis and turns around at the
  • If the multiplicity of a zero is ODD, then the graph crosses the x-axis at the zero.

Turning Points

  • The graph of a polynomial has at most n-1

Turning Points

  • The remainder theorem
  • If the polynomial f(x) is divided by x-c, then is a factor of f(x)
  • Rational Functions:

                f(X) =    the domain is all real # ‘s except those that make 9(X) = 0

A S x f(X)  0 : As  x approaches infinity f(X) approaches 0.

  • A S x  - , f(X)  : A S x approaches negative infinity, f(x) approaches 0.
  • xa+ : x approaches x from right
  • X a- : x approaches x from left
  • x: x approaches , that is x increases w/out bound
  • ][
  • ]\-p+’[
  • =/*;pX -: x approaches - , that is x decreases w/out bound

Locating Vertical Asymptotes

Example:  =  = x = - 3 and x = 3

                                Vertical asymptotes

Example:  = =  = x = 3

Example:  = Denominator can’t ever equal 0, so no asymptote.

Holes in Vertical Asymptotes

  • 1. If n<a, y=0 is the horizontal asymptote
  • 2. Id n=d, y = is the horizontal asymptote
  • 3. If n>d, the graph of f has no horizontal asymptote

EX:            Horiz asymptote: y=0

EX:            Horiz asymptote: Y = 4/2 or y = 2

EX:            No horizontal asymptote

Transformations  to graph  rational functions

f(x) =

Odd function: f(-x) = - f(x) origin symmetry                          Even function: f-(-x) =f (x)

                                                                Y-axis symmetry

                                                                +1 1. Right 2 units

                                                                      2. Up 1 unit

  • Example: f(x) =  

Graphic Rational Function

f(x) =

  1. Determine whether graph f has symmetry
  2. Find y-in+ by evaluating f (0)
  3. Find x in+ by solving p p(0) = 0
  4. Find vertical asymptotes by solving 9(0) = 0
  5. Find horizontal asymp by using rules
  6. P10+ at least 1 point between and beyond each x-in+ and vertical asymptote.
  7. graph
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