\n<\/h3>\n
- \n
- Concept of mapping and function\n<\/li>\n
- Domain, Co-domain of function – \u00a0\u00a0\u00a0\u00a0Types of mapping.\n<\/li>\n<\/ul>\n
\u00a0<\/p>\n
MAPPING
\n<\/h3>\nDefinition, Concept, Example and evaluation. <\/strong>
\n\tDefinition:<\/strong> This is the rule which assign an element x in set A to another unique element y in set B.
\n The set A is called the Domain while set B is the Co- domain
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se1.png\")
\n\tImage<\/strong>: This is the unique element in set B produced by an element in set A.
\nRange:<\/strong> This is the collection of all the images of the elements of the domain. <\/p>\n\u00a0 Using the diagram above: f(w)= g, f(x)= b, f(y)=f, f(z)=a a, b, f and g are the images of elements a,b,c and d respectively. Range = {a, b, f, g,} <\/p>\n
\u00a0 The rule which associates each element in set A to a unique element in set B is denoted by any of the following notations: f : A \u2192 B or f: A\u2192 B <\/p>\n
\u00a0
\n\u00a0
\n\u00a0
\n\u00a0FUNCTION<\/strong>: A function is a mapping whose co-domain is the set of numbers.
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se2.png\")
X F Y <\/p>\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0 Therefore, f (10) =4, f (9) =3 e.t.c <\/p>\n\u00a0Example 1: Given f(x) = 3x2<\/sup> + 2, find the values of (a) f (4) (b) f (-3) (c) f (-1\/2) <\/p>\n
\u00a0SOLUTION: <\/strong>
\n\t F(x) = 3x2<\/sup>+ 2 <\/p>\n- \n
- F(4), i.e x=4\n<\/li>\n<\/ol>\n
F(4) = 3(42<\/sup>) + 2 = 3(16) + 2
\n = 48 + 2
\n = 50 <\/p>\n- \n
- F(-3) = 3(-3)2<\/sup>+ 2\n<\/li>\n<\/ol>\n
= 3(9) +2 = 27 +2
\n = 29 <\/p>\n- \n
- F(-1\/2) = 3(-1\/2)2<\/sup>+ 2\n<\/li>\n<\/ol>\n
= 3(1\/4) + 2 = 3 + 2
\n 4
\n =11\/4.
\nExample 2: Determine the domain D of the mapping, g:x\u2192 2x2<\/sup> \u2013 1, if R= { 1,7,17} is the range and g is defined on D. SOLUTION<\/strong>:
\n g(x) = 2x2<\/sup>– 1, R = {1,7,17} To find the domain, when g(x) = 1, 1= 2x2<\/sup> -1 1+1 = 2x2<\/sup>
\n\t x2<\/sup> = 2\/2 x=1
\nWhen g(x) = 7,
\n 7 = 2x2<\/sup>-1
\n 7+1 = 2x2<\/sup> 8 =2x2<\/sup>
\n\t x2<\/sup>= 4, x= 2
\nWhen g(x) \u00a0\u00a0\u00a0\u00a0= 17, <\/p>\n- \n
- =x2<\/sup>-1\n<\/li>\n<\/ol>\n
17+1 = 2x2<\/sup><\/p>\n
- \n
- =x2<\/sup>\n\t\t<\/li>\n<\/ol>\n
x2<\/sup> = 9, x= 3 <\/p>\n
\u00a0Domain D ={1, 2,3} <\/p>\n
\u00a0<\/p>\n
EVALUATION
\n<\/h3>\n- \n
- Given f(x) = x2<\/sup>+ 4x +3 find the values of.\n<\/li>\n<\/ol>\n
\u00a0\u00a0\u00a0\u00a0(a) f(2) (b) f(\u00bd) (c) f(-3) <\/p>\n
\u00a0<\/p>\n
- \n
- Given that f(x) = ax + b and that f(2) = 7 ,f(3) = 12. Find a and b.\n<\/li>\n<\/ol>\n
\u00a0
\n\u00a0<\/p>\nTYPES OF MAPPING
\n<\/h3>\nOne-One mapping:<\/strong> A mapping is one-one if different elements in the domain have different images in the co- domain. If x1<\/sub>= x2 then<\/sub> f(x1<\/sub>) = f(x2<\/sub>) <\/p>\n
\u00a0 A 2X+3 B
\n -12
\n\t\t\t<\/sub>-51
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se3.png\")
3 4
\n\t\t\t<\/strong>
\n\tOnto Mapping<\/strong>: A mapping is onto if every element of the co- domain is at least an image of elements in the domain. E.g Let A = {-1, 0, 1} f : A \u2192 A be a mapping defined by f(x)= x3<\/sup>. <\/p>\n\u00a0 A F=X3<\/sup> B
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se4.png\")
\n\t \u00a0\u00a0\u00a0\u00a0
\nThe mapping is onto and one-one.
\n NB: In an onto mapping, the range is the same as the co- domain.
\nIdentity Mapping:<\/strong> This is a mapping which takes an element onto itself. If f: x\u2192 x is a mapping such that f(x) = x for all x \u20ac X. <\/p>\n\u00a0 \u00a0\u00a0\u00a0\u00a0
\n X X
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se5.png\")
\n\tThe mapping is one \u2013one and onto. It has a unique property that the domain, the co-domain and the range are equal. <\/p>\n\u00a0Constant Mapping<\/strong>: This is the mapping which assigns every element in the domain to the same image in the co- domain.
\n X Y
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se6.png\")
\n\t The range of a constant mapping consists of only one element. <\/p>\n\u00a0Important Notes:
\n1.
\n X F Y
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se7.png\")
\n\tThe relation F above is not a mapping because element q in X has no image in Y. <\/p>\n\u00a0
\n\u00a02.
\n A g B
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se8.png\")
<\/p>\n\u00a0The relation is not a mapping because element z in the domain has two images in the co \u2013domain. <\/p>\n
\u00a0<\/p>\n
EVALUATION
\n<\/h3>\n1. \u00a0\u00a0\u00a0\u00a0Given the mapping diagram below:
\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se9.png\")
X P Y <\/p>\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0
\n\u00a0 (a). Determine the rule of the mapping <\/p>\n- \n
- Is the mapping one- one? Is it onto?\n<\/li>\n
- What is the range of the mapping?\n<\/li>\n<\/ol>\n
\u00a0<\/p>\n
GENERAL EVALUATION
\n<\/h3>\n- \n
- Solve the system of equation; 2x + y<\/sup> =32, 33y \u2013 x<\/sup> = 27\n<\/li>\n
- Given h(x) = x3<\/sup>-6x2<\/sup> \u2013 3x +5 find the values of.\n<\/li>\n<\/ol>\n
\u00a0\u00a0\u00a0\u00a0(a) h(-2) (b) h(-\u00bd) (c) h(3) <\/p>\n
- \n
- Given that g(x) = 2p – q and that g(2) = 20 ,g(-3) = 15. Find p and q.\n<\/li>\n
- Given the functions h(y) = 3y2<\/sup> \u2013y+5, p(y) = 6y3<\/sup> + 7y2<\/sup>+7y+15. Simplify, as far as possible, the expressions\n<\/li>\n<\/ol>\n
(a) 3h(y) – p(y) (b) h(y) p(y) (c) h(y)\/p(y) <\/p>\n
\u00a0READING ASSIGNMENT<\/strong>: Read Mapping, Further Mathematics Project 2, and page 25- 35. <\/p>\n
\u00a0<\/p>\n
WEEKEND ASSIGNMENT
\n<\/h3>\n- \n
- If every element in the domain have different image I the co-domain, such type of mapping is called ——-\n<\/li>\n<\/ol>\n
(a) constant mapping (b) onto mapping (c) one- to \u2013 one mapping <\/p>\n
- \n
- A mapping f is called —— if every element of the co-domain is an image of at least one element in the domain (a) constant mapping (b) onto mapping (c) one- to \u2013 one mapping 3. Given f(y) = px<\/sup> and f (3) = 81, determine the value of x.\n<\/li>\n<\/ol>\n
A -4 B 27 C 4
\n 4 The rule that assign an element to two or non-empty set is (a) logic (b) set (c) mapping 5 If f is a function defined by f(x) = 2x2 <\/sup>– 3, find f(-3). A. -15 B 18 C. 15
\n \u00a0\u00a0\u00a0\u00a0 <\/p>\n\u00a0\u00a0\u00a0\u00a0THEORY
\n<\/h3>\n- \n
![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se10.png\")
Determine the domain D of the mapping f: x 2x \u2013 2, if c = { -3, -1, 5 } is range and f is defined on D\n<\/li>\n![\"\"\/](\"https:\/\/ecolebooks.com\/nigeria\/wp-content\/uploads\/9jalessonsimages\/100223_1032_Week5SS1Se11.png\")
Given that h: x x2<\/sup> + 2x \u2013 3 is a mapping defined on the set A = { -1, 0, 1, 2}. Find the range of h.
\n\t\t\t\t<\/strong>\n\t\t<\/li>\n<\/ol>\n\u00a0
\n\t\t\t<\/strong>
\n\u00a0<\/p>\n","protected":false},"excerpt":{"rendered":"\u00a0 WEEK FIVE \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0 \u00a0\u00a0\u00a0\u00a0DATE\u2026\u2026\u2026\u2026\u2026 MAPPING AND…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1,188],"tags":[],"class_list":["post-2172","post","type-post","status-publish","format-standard","hentry","category-posts","category-second-term-ss1-further-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2172","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/comments?post=2172"}],"version-history":[{"count":2,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2172\/revisions"}],"predecessor-version":[{"id":2174,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/posts\/2172\/revisions\/2174"}],"wp:attachment":[{"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/media?parent=2172"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/categories?post=2172"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/ecolebooks.com\/nigeria\/wp-json\/wp\/v2\/tags?post=2172"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
- A mapping f is called —— if every element of the co-domain is an image of at least one element in the domain (a) constant mapping (b) onto mapping (c) one- to \u2013 one mapping 3. Given f(y) = px<\/sup> and f (3) = 81, determine the value of x.\n<\/li>\n<\/ol>\n
- If every element in the domain have different image I the co-domain, such type of mapping is called ——-\n<\/li>\n<\/ol>\n
- Given h(x) = x3<\/sup>-6x2<\/sup> \u2013 3x +5 find the values of.\n<\/li>\n<\/ol>\n
- Solve the system of equation; 2x + y<\/sup> =32, 33y \u2013 x<\/sup> = 27\n<\/li>\n
- Given that f(x) = ax + b and that f(2) = 7 ,f(3) = 12. Find a and b.\n<\/li>\n<\/ol>\n
- Given f(x) = x2<\/sup>+ 4x +3 find the values of.\n<\/li>\n<\/ol>\n
- =x2<\/sup>\n\t\t<\/li>\n<\/ol>\n
- =x2<\/sup>-1\n<\/li>\n<\/ol>\n
- F(-1\/2) = 3(-1\/2)2<\/sup>+ 2\n<\/li>\n<\/ol>\n
- F(-3) = 3(-3)2<\/sup>+ 2\n<\/li>\n<\/ol>\n
- F(4), i.e x=4\n<\/li>\n<\/ol>\n