University:
Camosun College
Course:
NURS132 | Promoting Health and Wellbeing
Academic year:

2024
Views:

135

Pages:

5
Author:

Aysha A.

LAB-18 - FUNCTIONS Aim: To visualise one to one and onto function geomehically • To restrict the domain and co-duman af function so as to make it a bijectio To visualise composition of two function geometrically. Concepts: one to one onle functions. Activity 14.1 Procedure. one to one and onto Function •Draw the graph of fox)=x2 create a slider a and plot the point (014) Draw a line through the point and Perpendicular to the yaxis plot the points of intersection of the line with curve • It for any valle of a. the line Melts the love at more than one Point can we say wether the functio onen Answes. Not one to one. Differens elemene har Sani image • if for all value of 'a', the line meets the curve atleast one points can we say wether the function onto or not why? Answer: Yes range and codomain are same Using above applet, say wheather the function R R defined above is one to one or onto. Answu: no. • Heeping above ideas in mind, une can say whether a function is one to one or onto by observing its graph, even without drawing the horizontal line. save the file as Activity 14.1 Aclivity 11.2. one to one and onto huntron-2 • Praw the graphs of the following functions defined from R -> R. and Say whether they allone Or un to. Find the range of the function in each case Answu: Function one-one onto range Domare Loduna 1)x42 6 no [2120) R 11) x³-3x213 NO Yes R R R ilt) 3 sin x No NO [3.3] R R • The following function cue defineel fr了 a subsel of the set of real numbers. Say whither they ale one to one or onto. find their range 1) 1: R- {3}R-{i} de fined by f(x) = x-2 (1) J: [-1,1][-] defined by 2x-3 +(x)= 11) f: R-R defined by x+2 fcx)= x Function one-one Onto Range Domain calumin P(x)-2-2 x-3 Yes Yes R-{1} R-{3} -{1} x +3 Yes No Elly R x+2 Yes NO [11] R R • what is the pecullarity of the range of an the range onto function Activity 18.3 Bijective functions. • Draw the graph of the function f: RR defined by f(x)=x2+1 i's in one-one or ontor Answd: Not one-one, onut onto •Redefine the function by restrictiong it clone So that it becomes one-one Answer. Domain= [120) • Redefine the function by restricting its domain so that it becomes onto Answel. Codomaun = [1,00). So the functions: [0,00)→ [1,00) detired by Pcx) = x²- is a bijection • Draw the graph of the above function Cuse input command if (x >= 0x2+1) os it (x>= 01f) or function (fio, infinity)). • If we detine 1. (-2010] → [1,00) then also it becames a bijelion. Draw the graph of this function. Restrict domain and co-domain of the following functions so that they becomes bijectiom. Answel Junction 1)12-21 Domain [2100) 11) x³-3x+3 (100) (sinx) co-domain. [0,0) [10) [01] •For each of above functions find one more domain which make them one to one Draw the corresponding graphs Answer