Question

Dibuje las gráficas de las siguientes formas de f(t): (a) f(t) – f(t)U(t –1) (b) f(t – 2) U(t – 2) (c) f(t)U(t – 2) (d) f(t) – f(t) U(t – 2) (e) f(t) U(t – 1.) – f(t) U(t – 3) (f) f(t – 2)U(t – 2) – f(t – 2) U(t – 4)

Draw the graphs of the following forms of f(t)

Answer 1

( 1) Solution Let fit) be a given function and alt-a) be the unit step function defined allt-a)= It ta Now, consider the graph of fit as given below [taking such a graph function, flt), is specified] Just for illustration as no 3 and graph of Ult-a) is as follows 6

(2) (a) fit) - f(t) 2(t-1) Here fit) UCE) = it 177 S fito fit). I 1k 127 o ELI flt) I tal . flt) - f (t) U (E-1) = flt) - o It ㅏ시 Iflt) - f(t) it t², I S fit) { If 121 It +21. Hence graph of flt) - flt) UCH-t is, 3 2 -4 -3 -2 1 (b) f(4-2) 1 ct-2) obtained by f(t-2) the function whose graph is a shifting two units to the right the graph of fit to two units night. le, the ft 2) is, is graph of 2 Y = S(1-2) 2. 3

(3) allt-2) is 2 3 LP and Fit - 2) 21 (4-2) = Fitz) o 16 122 F(x-2). I 1 +22 2F (6-2) 16 +32 Hence the graph of flt-2) 1(E-2) 15 gru-2) 21 (1-2) FIE) U CE-2) f(t) U (E-2) = It E22 S fit). F(t). I O it 122 FIE) if t22

Hence the graph of f(t). 2114-2) is, 2 y = f(t) 214-2) 1 (d) f(t) - F(t) 21 (4-2) f(t) uct-2) = S fee FCE). O 16 t22 it t22 (4). 13 122 FLE to2 then, f(t)-f(4) 2(t-2) = f (I) - o +42 F(t)- flt) 16 t22 flt it +42 16 t>2 Honce the graph of flt) FIE) auct-2) is, y y = f(t) - F4321 (1-2) < -2 1 1 2 3 t T

(5) (e) f(t) (t-1) - flt) alt-3) O. FU) tal flt) 2 (4-1) = 1 flu tal tal Fit) 16 f (t) 2(t-3) = 11 +23 ६२॥ SEHO (FH). So it tc3 [su Fu) it t=3 Then, fit) u (t-1)-f(t) 2 (4-3) = 77 40-(AJ Ist<3 Est al (AJ- (A))) tal flt) If K13 18 t23 Hence the graph Fuck-D-flt) (E-3) is, 3 2 0 3 -2 2 -4 3

(6) flt-2) ou (4-2) - f (t-2) 2 (4-4) f(t-2) a (t-2) = it t22 fit-2)-1 It t=2 O 14 t22 t> fit-2) 21CF-4) flt-2). If t24 16 O t24 fit-2). I 14 t> 4 - { flt-2 a t> 4 Then tca flt-2) 2 (4-2) - f (+-2) 21 (1-4) = fit-2) 16 2LE24 It 4st Hence the graph of flt-2) 4 (E-2) - F(E-2) 21Ct-4) y = f(4-2) 4 (6-2) - 1182) raf-4) 3 -4 o - 2 3 A 5 6 -- Please ref the graph of f(x-2) chrown in part (6)

Please share your feedback. Thanking you in advance.