Funksies en Verwantskappe
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1 UITDRUKKINGS
2 Funksies en Verwantskappe n funksie is n verhouding tussen waardes Elke inset waarde het n spesifieke uitset waarde a) Bereken die -waardes (uitset) b) Bereken die -waarde (inset) Die vloeidiagram
3 Die tabel a) Bereken die -waardes (uitset) b) Bereken die -waarde (inset)
4 HUISWERK
5 REëLS Gee die verwantskap / reël vir die uitset waardes in algebraïese vorm Y = Gee die verwantskap / reël vir die uitset waardes in algebraïese vorm en bereken A en B B A 4 Y =
6 HUISWERK
7 EKWIVALENTE VORMS Twee uitdrukkings kan ekwivalent wees indien hulle uitset waardes spesifieke inset waardes het. Piet dink aan n getal, maal dit met 5 en tel 10 b. a) Ontwerp n vloeidiagram om die verhouding voor te stel X b) Skrf die verhouding in algebraiiese vorm 5 10 c) Voltooi die tabel om uit te vind watter uitdrukkings is ekwivalent ( ) d) Skrf al die ekwivalente uitdrukkings neer ( ) e) Bereken 5( ) en 5 10as =
8 HUISWERK
9 ALGEBRAIESE UITDRUKKINGS SOM VAN VERSKIL VAN PRODUK VAN KWOSIENT VAN (MEER, GROTER, PLUS) (MINDER, KORTER, KLEINER, MINUS) (MAAL, KEER GROTER) (DEEL, KEER KLEINER) * Die maalteken word nie altd gebruik nie (veranderlikes word langs mekaar geskrf) * J skrf die veranderlikes altd in alfabetiese orde * 1 n word geskrf as 1n of n * n n n is nie gelk aan n + n + n nie * In plaas van skrf ons 5 5
10 * Terme word gekei met n + of n - * Hakkie,s maal en deel groepeer die terme (1 term) # Die som van 5 en n getal? # Die verskil tussen 5 en n getal? 5 # Die produk van 5 en n getal? # Die kwosient van 5 met n getal? # 4 Hoeveel terme? a b ( a b) 4 6 # k Hoeveel terme? # ( 5 7) 4 Hoeveel terme? 5 k 4
11 # 4 + is n numeriese uitdrukking # + is n algebraiese uitdrukking (bevat veranderlikes) # n uitdrukking het geen =, < of > # Die koeffisient van n getal is die getal / gedeelte wat met die veranderlike gemaal word (nie noodwendig net die getal vooraan nie) a) Gee die koeffisient van in b) Gee die koeffisient van in c) Gee die koeffisient van in d) Gee die koeffisient van in b 4 7 b
12 a) Skrf die uitdrukking in dalende magte van, en gee die graad in b) Skrf die uitdrukking in stgende magte van, en gee die graad in Graad in is Graad in is 4 # Konstante getal: Die getal sonder n veranderlike # Dalende magte: Rangskik van groot na klein # Stgende magte: Rangskik van klein na groot # Die graad in is die hoogste eksponent vir n term met n in.
13 HUISWERK
14 OPTEL EN AFTREK VAN UITDRUKKINGS Gelksoortige terme is terme met dieselfde veranderlike (grondtal) en eksponent 5 5a ab ba 8a en en a 4 is gelksoortig is gelksoortig en is gelksoortig J mag slegs gelksoortige terme b mekaar tel of aftrek Wanneer opgetel of afgetrek word, bl die eksponente onveranderd
15
16 TEL OP / TREK AF SLEGS GELYKSOORTIGE TERME!!!!! Plus a 4a 5a a 1 en a 4a 5 a 4a 5a a 1 a 4a 5 6a a
17 a 5b c a 6b Trek Af van c a 6b c a 6b c 5a 7 b ( a 5b c) a Trek Af van ( 7) b c
18 Vanaf 8 trek 4 5 af 8 (4 5)
19 HUISWERK
20 MAAL UITDRUKKINGS NB!! ( + ) ( + ) = ( + ) ( - ) ( - ) = ( + ) ( + ) ( - ) = ( - ) NB!! ( + ) ( + ) = ( + ) ( - ) ( - ) = ( + ) ( + ) ( - ) = ( - ) ( 5) (8 z) () (4z) 5 16z 4 1z 9 8z ( ) ( ) ( 6 )
21 HUISWERK
22 DEEL UITDRUKKINGS NB!! ( + ) ( + ) = ( + ) ( - ) ( - ) = ( + ) ( + ) ( - ) = ( - ) + 6 = + 6 = = = 4 + 1
23 HUISWERK
24 VIERKANTE EN DERDEMAGTE Vereenvoudig: ( a b ) 4 4 9a b ( b ) 6 b 4 7( a c 4 8 7a c ) ( a b) a 9 b 10b ( b) 17b ( b 5 ) 6 10b 7b ( b 6b 15 7b ( 4 ) b ) ( ) 4 ( ) ( ) 1 1 4b (8b ) b b ( a ) 5a 6 6 a 5a 6 4a ( m n) ( mn 6 m n 9 n 11 m 9 m n )
25 HUISWERK
26 EXPRESSIONS
27 FUNCTIONS AND RELATIONSHIPS A function is a relationship between variables Each input value has a specific output value a) Calculate the output values b) Calculate the input value Flow chart
28 THE TABLE a) Calculate the output values b) Calculate the input value
29 HOME WORK
30 RULES Give the relationship or rule for calculating the output value Y = Give the relationship or rule for calculating the output value B A 4 Y =
31 HOME WORK
32 EQUIVALENT FORMS Two equations can be equivalent, if their output values are the same Peter thinks of a number, multiplies with 5 and add 10. a) Set up a flow chart X b) Give a rule 5 10 c) Complete table ( ) d) Which are equivalent ( ) e) Calculate 5( ) and 5 10if =
33 HOME WORK
34 ALGEBRAIC EXPRESSIONS SUM OF DIFFERENCE OF PRODUCT OF QUOTIENT OF (MORE, GREATER, ADD) (LESS, SHORTER,SMALLER, SUBTRACT) (MULTIPLY, TIMES GREATER) (DIVIDE, TIMES SMALLER) * Variables are written net to each other without a multipl sign * Variables are written in alphabetical order * 1 n is written as 1n or n * n n n is not the same as n + n + n * In stead of we write 5 5
35 EXPRESSIONS AND TERMS * Terms are separated b a n + or n - * Brackets, multipl, and divide group terms as one # The sum of 5 and a number? # The difference of 5 and a number? 5 # The product of 5 and a number? # The quotient of 5 with a number? # 4 How man terms? a b ( a b) 4 6 # k How man terms? # ( 5 7) 4 How man terms? 5 k 4
36 # 4 + is a numerical epression # + is an algebraic epression # a epression has no =, < or > # The quotient of a number is the part left over after division. a) Give the coefficient of in b) Give the coefficient of in c) Give the coefficient of in d) Give the coefficient of in b 4 7 b
37 a) Write in descending order of, and give the degree in b) Write in ascending order of and give the degree in Degree in is Degree in is 4 # Constant: The number without variable # Descending order: Big to small # Ascending order: Small to big # Degree in is the highest eponent of this variable.
38 HOME WORK
39 ADD AND SUBTREACT EXPRESSIONS Like terms has the same base and eponent 5 ab ba 5a 8a and and a 4 are like terms are like terms and are like terms You ma onl add/subtract like terms, and the eponent sta unchanged
40 a 4a Add 1 a 4a 5a a 1 a 4a 5 6a a 5a a en a 4a 5
41 a 5b c a 6b Subtract from c a 6b c a 6b c 5a 7 b ( a 5b c) a Subtract from ( 7) b c
42 from 8 subtract (4 5)
43 HOME WORK
44 MULTIPLY EXPRESSIONS NB!! ( + ) ( + ) = ( + ) ( - ) ( - ) = ( + ) ( + ) ( - ) = ( - ) NB!! ( + ) ( + ) = ( + ) ( - ) ( - ) = ( + ) ( + ) ( - ) = ( - ) ( 5) (8 z) () (4z) 5 16z 4 1z 9 8z ( ) ( ) ( 6 )
45 HOME WORK
46 DIVIDE EXPRESSIONS NB!! ( + ) ( + ) = ( + ) ( - ) ( - ) = ( + ) ( + ) ( - ) = ( - ) + 6 = + 6 = = = 4 + 1
47 HOME WORK
48 SQUARES AND CUBES Simplif : ( a b ) 4 4 9a b ( b ) 6 b 4 7( a c 4 8 7a c ) ( a b) a 9 b 10b ( b) 17b ( b 5 ) 6 10b 7b ( b 6b 15 7b ( 4 ) b ) ( ) 4 ( ) ( ) 1 1 4b (8b ) b b ( a ) 5a 6 6 a 5a 6 4a ( m n) ( mn 6 m n 9 n 11 m 9 m n )
49 HOME WORK
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