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In: Business and Management

Submitted By eddo
Words 561
Pages 3
Managerial Mathematics(QQM 1023)
Tutorial 2 – Introduction to Function

1. Which of the following equations define y as a function of x?

a) y = 3x + 1 b) y = 2x2 c) y = 5 d) y = 2x e) x = 3

f) y2 = x g) y = x3 h) y = [pic] i) y = x j) y = [pic]

2. Determine types of function for the following equations: a) f(x) = 2 b) g(x) = [pic] c) f(x) = 4 – x d) f(x) = 2x e) g(x) = x2 + 3x f) h(x) = 2x g) h(x) = ex h) g(x) = x2 i) h(x) = [pic]

j) h(x) = [pic]

3. Find the values for each function based on the inputs given:

a) f(x) = 3x – 5, f(-1) and f(0) b) g(x) = x2 – 3x, g(4) and g(-2) + g(0)

c) f(t) = [pic], f(2) and f(0) d) g(t) = 2t , g(3) and g(0) – g(1)

e) h(x) = [pic] , h(-1) and h(3) f) h(x) =[pic] , h(-3) and h(1) + h(0)

g) g(x) = [pic] , g(1) and g(-1) h) f(x) = [pic] , f(1) and f(9) – f(-1)

i) g(x) = [pic] , g(2) and g(0) + g(-2) j) f(x) = 5 , f(0) and f(-1) – f(5)

4. Find the domain of each function: a) f(x) = [pic] b) h(x) = [pic] c) g(x) = [pic] d) g(x) = [pic] e) h(x) = [pic] f) f(x) = [pic] g) f(x) =[pic] h) h(x) = [pic] i) f(t) = 4t2 – 5 j) f(x) = 4 k) g(x) = [pic] l) f(x) =[pic] m) f(x) = [pic] n) h(x) = [pic]

5. Based on the graphs, determine the domain and range of the given functions. a) y = x + 1 b) y = x2 c) y = [pic] d) y = x2 - 9

e) x + y = 1 f) y = 4 – x2 g) y = 2 h) f(x) = [pic]

6. If a RM 30,000 machine depreciates 2% from its original value each year, find a function f that expresses the machine’s value V after t years have elapsed.


1 a) b) c) d) g) h) i) j)

2 a) constant b) rational c) linear d) linear e) quadratic f) exponential g) exponent h) quadratic i) compound j) linear

3 a) –8 and –5 b) 4 and 10 c) [pic] and 0 d) 8 and –1 e) 1 and 3 f) 2 and 9 g) 2 and 0 h) 9 and 10 i ) 4 and –4 j) 5 and 0

4 a) x ( R, x ( 0 b) x ( R, x ( [pic] c) x ( R d) x ( R, x ( 0, x ( 1 e) x ( R, x ( 3 f) x ( R, x ( -1, x ( -5 g) x ( R, x > 0 h) x ( R i) t ( R j) x ( R k) x ( R, x ( -8 l) 1 ( x ( 3 m) x ( R, x ( [pic] n) x ( R 5 a) D : x ( R , J : y ( R b) D : x ( R , J : y ( 0 c) D : x ( R, x ( 0 , J : y ( R, y ( 0 d) D : x ( R , J : y ( -9 e) D : x ( R , J : y ( R f) D : x ( R , J : y ( 4 g) D : x ( R , J : y = 2 h) D : x ( 0 , J : 0 ( y ( 2

6 [pic]



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Pagsubok at Pag-Asa

...Philosophy 103 Finals HIWAGA NG PAGSUBOK AT PAG-ASA Ang buhay ng tao kahit na mukhang normal ay isang palagiang pagsubok To be human, to be man is to experience trials Life, itself, is tragic – its a trial Ang pagsubok ay maaaring ihambing sa: kadiliman pagkabilanggo *sa pagdanas ng pagsubok, madalas maramdaman ng indibidwal ang kawalan ng kalayaan – ang indibidwal ay nalilimita ng mga pangyayari kung saan maraming hindi maaaring gawin, nakagapos siya sa di-ginustong uri ng pag-iral *sa kabilang dako, ang pag-asa ay tila isang liwanag na siyang tugon sa kadilimang kinasasangkutan ng indibidwal *kapag lumampas sa itinakdang oras (deadline) ang pagtagal ng pagsubok, nalulugmok ang inidibidwal sa estado ng pagtataboy-ng-pag-asa (despair) Pagtataboy sa Pag-asa: pagtatakwil sa sarila, sa iba at sa Diyos alienation sa pagsuko ng tao: nagagayuma at inaasam na wasakin ang sarili enchantment: inaasahang pag-ulit ng kondisyon o ang hindi pag-alis sa kaniyang kinalalagyan ang pagkagayuma na ito ang nagdudulot sa indibidwal na paniwalaang hindi na gumagalaw ang panahon nawawala ang kaniyang personal na ritmo at pasensiya from this disintegration begins (ang inaasahan niya sa kinabukasan ay binabase niya sa pagkabigo ng nakaraan, walang kalalabasan) solitude: pagsara ng sarili sa iba, pag-iisa Ang pagsuko ay isang pag-indibidwal na gawain. Sa kabilang dako, pag-asa ay isang komunikasyon sa ibang tao. Ang madalas na anyo ng buhay ng tao ay ang pagkabilanggo...

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