Lineære funktioner emne opgave

!"#$%&!'()*"+&,-..$&& & /"-.0"-'(&1& ;0$.)<9"#.&=&>&?'$.@3.&A5$(-')$.3& 2"3456&7"$8.*69:0$"6'50&

&

!"#$%&$'()#*+",#$&



  • B.$.3.*-&)0&A5$(-')$6C.93.C.-&D6'8.&EF& • G"A4@$9'9&#"3'"C.*&)9&"A4@$9'9&#"3'"C.*&D,'8.&EF& • H.A'$'-')$60@$98.&)9&#@38'0@$98.&D,'8.&EF& • H.$&9.$.3.**.&A)36(3'A-&A)3&.$&*'$.@3&A5$(-')$&D6'8.&IF& • 2-&-.9$.&.$&*'$.@3&A5$(-')$J&$K3&A)36(3'A-.$&.3&(.$8-&D,'8.&L&&F& • 2-&C.6-.00.&A)36(3'A-.$J&$K3&-)&<5$(-.3&(.$8.6&D6'8.&M&F& • 7#"8&.3&.-&$5*<5$(-&)9&4#)38"$&A'$8.3&0"$&8.-N&D6'8.&OF& • 7#)38"$&A'$8.3&+.9&6(@3'$96<5$(-.-P&D,'8.&QF&& ;3&8.3&"*-'8&<3@R'6-&.-&6(@3'$96<5$(-P&  • ;(6"(-.& • ?'$.@3.&3.93.66')$&

=& &

!"#$%&!'()*"+&,-..$&& &

/"-.0"-'(&1& ;0$.)<9"#.&=&>&?'$.@3.&A5$(-')$.3&

2"3456&7"$8.*69:0$"6'50&

H.*&=&

B.$.3.*-&)0&A5$(-')$6C.93.C.-&

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

E& &

!"#$%&!'()*"+&,-..$&& &

/"-.0"-'(&1& ;0$.)<9"#.&=&>&?'$.@3.&A5$(-')$.3&

2"3456&7"$8.*69:0$"6'50&

& 6)0&0"$&("$&6.&.3&#@38'0@$98.$&A3"&[&-'*&=[[[&8"&:&'((.&.3&*"#.3.&.**.3&4Y+.3.&.$8&8.-N&& /"$&("$&)96K&6.&"-&"**.&T`.3$.&'&0'$56&)9&"**.&T`.3$.&4Y+.3.&.$8&=[&.3&#@(J&8"&8.&'((.&.3&3.*.#"$-.J&8.-&.3& 8.A'$"-')$60@$98.$&

H.$&9.$.3.**.&A)36(3'A-&A)3&.$&*'$.@3&A5$(-')$&

a&8.--.&"A6$'-&#'*&+.9&A)3-@**.&)0&8.$&9.$.3.**.&A)36(3'A-&A)3&.$&*'$.@3&A5$(-')$N&Z)36(3'A-.$&A)3&.$&*'$.@3& A5$(-')$&("$&6(3'#.6&<K&AY*9.$8.&0K8.%& !"#$%&%'#%(%)% 2&.3&4#)3&0.9.-&#)3.6&:&#)(6.3&0.8&$K3&#)3.6&T&#)(6.3&.$&9"$9N&b&.3&6K&6(@3'$9.$&0.8&:&"(6.$N&&D"&)9&C& 4)*8.3&<*"86.$&A)3&8.&-"*&#'&'((.&(.$8.3&.$8$5F& !.8.$A)3&6.6&.$&'**56-3"-')$J&8.3&#'6.3&C.-:8$'$9.$&"A&"&)9&CN&

I& &

!"#$%&!'()*"+&,-..$&& &

/"-.0"-'(&1& ;0$.)<9"#.&=&>&?'$.@3.&A5$(-')$.3&

2"3456&7"$8.*69:0$"6'50&

& '&6-.8.-&A)3&"&4"3&#'&*"9-&E&'$8J&)9&'&6-.8.-&A)3&C&4"3&#'&*"9-&L&'$8N&S.8&LJ&[&4"3&+.9&*"9-&.-&<5$(-&#.8&$"#$&CJ&)9& 8.-&.3&8.3&4#)3&8.3&6(@3'$9&0.8&:&"(6.$J&)9&8.30.8&("$&#'&6.&"-&CW&6(@3'$9&0.8&:&"(6.$N&c.9&4"3&)96K& 6(3.#.-&.$&-.(6-&d=&58&)9&E&)<d&H.-&C.#'6.3&"-&"&4#)3&0.9.-&8.$&6-'9.3J&$K3&T&#)(6.3&.$&& &

2-&-.9$.&.$&*'$.@3&A5$(-')$J&$K3&A)36(3'A-.$&.3&(.$8-&

c.9&#'*&$5&A)3(*"3.J&4#)38"$&.$&*'$.@3&A5$(-')$&-.9$.6J&$K3&A)36(3'A-.$&.3&(.$8-N&c.9&4"3&*@3-&-3.&A)36(.**'9.& 0.-)8.3J&6)0&+.9&"**.&#.8&3.8.9Y3.&A)3%& \ \ \ ,-Y--.<5$(-.3& H'3.(-.&#4"N&"&)9&C& ea\!6<'3.&

c.9&#'*&#.8&"**.&-3.&0.-)8.3&-"9.&589"$96<5$(-&'&6"00.&A5$(-')$J&$.0*'9&A5$(-')$.$&ADTF&W&ETfL& & ,-Y--.<5$(-.3& &

S)3.6&6'*8.C.$&6.6&5$8.3J&85&("$&#.8&4+@*<&"A&6'0<*.&3.9$.6-:((.3&A'$8.&58&"A&4#'*(.$&A5$(-')$&85&4"3N&H5& 6("*&6-"3-.&0.8&#@*9.&8'$.&T&#@38'.3J&8.&.3&5"A4@$9'9.&6K&#'&("$&#@*9.&"**.&-"*N&,)0&85&("$&6.&5$8.3J&4"3&#'& *"9-&8.&#@38'.3&'&8.$&Y#.36-.&-"C.*&"A&6'*8.C.$.-N&& & T& &&&&&&&&&&&&&&&&:& & E& Q& L& =E& M& =M& Q& E[&

L& &

!"#$%&!'()*"+&,-..$&& &

/"-.0"-'(&1& ;0$.)<9"#.&=&>&?'$.@3.&A5$(-')$.3&

2"3456&7"$8.*69:0$"6'50&

!5&6("*&85&583.9$.&4#"8&8.3&6("*&6-K&'&:&("66.3$.N&H.-&9Y3&85&#.8&"-&'$86@--.&T&'&A5$(-')$.$N&ZN.(6h&]"66.&=W&& :WEXEf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fLN&S'&("$&C359.&8.$&4.3&A)3&"-&9Y3.&8.-&$.00.3.h&!"#$%&%'#%(%)*% H.-&AY36-.&#'&6("*&9Y3.&.3&"-&A'$8.&<5$(-&C&#)3.6&())38'$"-N&7#'*(.-&'&#)3.6&-'*A@*8.&.3&D[JLF&&8.3&[email protected]&#'& #)3.6&AY36-.&<5$(-N&H.-&$@6-.&#'&6("*&9Y3.&.3&"-&A'$8.&#)3.6&$@6-.&<5$(-&.3N&H.-&9Y3&#'&#.8&"-&('99.&<K& "D4@*8$'$9.$F&6)0&EN&H.-&#'*&6'9.J&"-&#'&6("*&58&A3"&<5$(-&CJ&6("*&9K3&'$8&58&)9&8.3.A-.3&E&)<N&,K&A'$8.3&#'& #)3.6&$@6-.&<5$(-&D=JMFNS'&("$&$5&C*)-&A)3C'$8.&8.0&0.8&4+@*<&A3"&.$&*'$."*N&& &

N& ea\!6<'3.&

&

ea\!6<'3.&.3&8.$&$.00.6-.&)9&453-'96-.&0K8.&"-&-.9$.&.$&A5$(-')$&8.-&("$&9Y3.6&0.8&AK&(*'(N&/"$&6("*& 6-"3-.&0.8&"-&KC$.&.-&$:-&8)(50.$-&)9&(*'((.&-'*AY+&93"AN&i#.$&)#.3&93"A.$&.3&8.3&.$&C)(6&4#)3&8.3&6-K3& A=DTFWN& a&8.$&C)(6&6("*&#'&'$86@--.&8.$&A5$(-')$&#'&#'*&4"#.&3.9$.-N&a&#)3.6&-'*A@*8.&6(3'#.3&#'&ETfL&)9&8.-&#'*&6.&6K8"$&

g& &

!"#$%&!'()*"+&,-..$&& & 58%&

/"-.0"-'(&1& ;0$.)<9"#.&=&>&?'$.@3.&A5$(-')$.3&

2"3456&7"$8.*69:0$"6'50&

S'&-3:((.3&8.3.A-.3&.$-.3&)9&A3.0&()00.3&#)3.6&-.9$'$9%&

&

2-&C.6-.00.&A)36(3'A-.$J&$K3&-)&<5$(-.3&(.$8.6&

c.9&#'*&#'6.&4#)38"$&0"$&A'$8.3&A)36(3'A-.$&0.8&I&0.-)8.3J&)9&+.9&#'*&C359.&<5$(-.3$.&EJL&)9&LJQ& 2A*@6$'$9& H5&'[email protected]&<5$(-.3$.&)9&8.3.A-.3&A)3C'$8.3&8.0&0.8&.$&6-3.9N&!K3&85&4"3&9+)3-&8.-&9@*8.3&8.-&)0&"-& A'$8.&"&)9&C&'&8.$&9.$.3.**.&A)36(3'A-&ADTFW"TfC& S'&6-"3-.3&0.8&"-&A'$8.&CJ&)9&8.-&.3&8.3&4#)3&A5$(-')$.$&6(@3&:&"(6.$N&H.-&9Y3&8.$&#.8&$5*&)9&8.3A)3&.3&CW[& S'&6("*&)96K&A'$8.&58&"A&4#"8&4@*8$'$96-"**.-D"F&.3N&H.-&("$&#'&$.0-&9Y3.&)9&8.-&9'3&"WEN&!5&4"3&#'&CK8.&#)3.6& "&)9&#)3.6&C&6K&$5&("$&#'&6(3'#.&A5$(-')$.$h&ADTFETf[&& & Z)30*.3&&& S'&C359.3&'9.$&EDTFJLD:=F&)9&LDTEFJQD:EFN&H.&A)30*.3&#'&6("*&C359.&.3 

 

&)9&CW:=\"XT&&&&&ZDTFW&&"TfC&

M& &

!"#$%&!'()*"+&,-..$&& &

/"-.0"-'(&1& ;0$.)<9"#.&=&>&?'$.@3.&A5$(-')$.3&

2"3456&7"$8.*69:0$"6'50&

S'&6("*&6-"3-.&0.8&"-&A'$8.&"&6K&8.3&<5--.3&#'&8.&#@38'.3&'$8&#'&6("*&C359. 

 

        &!5&