Question

Use the graph below to determine whether the statements about the function y=f(x) are true or false. Ay 10- 8- 6 -10 -8 -6 -4 -2 2 8 10

Answer 1

as soe 10 Ginen, 9 8 +6 4 5 10 -6 -5- ů, lim f(x) =9 X+-37 Statement is (TRUE The x Lim fla) is flou -9, means going close Xy-3t X=-3 but from Right Hand can -3, we the graph, the point Side of clearly from su as x gets close to point - from Right hand side, f(x) gets closer to X-9

So, tim f(x)=9 is TRUE X 4-3t Li) lim f(x) = 3 xor Statement is This FALSE Since, as. xo (ie x is approaching x-artis from L.H.S, to point 'o' on x the 'olon curne i closer to nalue le, as y arisa xo, f(x) approaches to lo 80, lim f(x)= 3 is FALSE *70- (iii) lim X700 768) lim fle) Xot the from gineu graph we have, lim f(a) al X30

and tim. f()=0 arot şie. ad x approaches to point 'o' from Right Hand Side (or from positine side) close to o) is close the ualue of y lim f(x) f(x) > is / TRUE lim X701 asot

llu) A limit, lins No a f(x) is said to exist lins f(x) lim f(x) a Wat from part (iii) we have f(x) lim flas zo Kyot lim f(x) exists lim X>0 270 So, the Stalement is TRUE (V) lim flow exists, then, ХЭa tim fala lim fla) lins fixe) xtat Xsa xtar we from part have tim f(x) = lim flat) = 0 X+02 Xtot lim f(x) f(x)=0 ХЭo So, the statement is TRUE o

(VVO Lim => 3 f(0) = 9 The Statement يد false. Since we have as to 3 x 3 from Left Hand from graph, approaches Side, le lim flos = 9 value of y is closer to 9. X-3

and as х approaches to 3 from Right becomes close to 3, is and Hand Side value of be ) O, lim Xat f( (a)= co kiss f(x) Susce, and, f(x) & tim lius f(x) X537 7337 7100 does not exist and Lim f(x) = 9 x +3 FALSE

(VI) lim f(x) = 6 X 6 as x to 16? ar false. This Statement is Since approaches to f and gets closer from Left Hand Side Negative Direction, nalue of flow is .( shown by a dark blue line on x-axis, the line shows that when we[3,6] value of f(x)=0) false, ६०) lim f(x) = 6 , us X>6