TRANSFORMATIONS OF EXPONENTIAL FUNCTIONS PRESENTATION 5 STUDENT WORKSHEET WITH SOLUTIONS

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St Edmund Campion Secondary School**We aren't endorsed by this school

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MATH MCR3UP

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Mathematics

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Dec 16, 2024

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Unit 3 -L5 TRANSFORMATIONS OF EXPONENTIAL FUNCTIONS STUDENT WORKSHEET 1) Describe the transformations that map the function y = 2* onto each of the following functions... a)y=2*-2 b) y = 2**3 )y =4 d)y=32"")+1 2) Create a sketch of each graph for each equation in question 1. (a table of values may help) a) b)

c) d) 3) Write the equation for the function that results from each transformation applied to the base function y = 5% a) translate down 3 units b) shift right 2 units c) translate left % unit d) shift up 1 unit and left 2.5 units

4) Describe the transformations that map the function y = 8* onto each function. a)y = (3)8" b) y = 8% c)y=—8% dy=8% 5) Write the equation for the function that results from each transformation applied to the base function y=7* a) reflect in the x-axis (vertical reflection) b) stretch vertically by a factor of 3 c) stretch horizontally by a factor of 2.4 d) reflect in the y-axis and stretch vertically by bafo 7 6) Sketch the graph of y = (— %) 2*~* by using y = 2* as the base and applying transformations.

7) Sketch the graph of y = 3795¥-1 — § by using y = 3* as the base and applying transformations. L AN e S e S S SR S S B S S S S SN S S S 8) a) Rewrite y = 9* using a base of 3. Describe how you can graph this function by transforming the graph of y = 3%, b) Rewrite y = 9* using a base of 81. Describe how you can graph this function by transforming the graph of y = 81*.

Answers 1) a) translate 2 units down b) translate 3 units left ¢) horizontal compression by a factor of i d) vertical stretch by a factor of 3, a translation 1 unit to the right and 1 unit up 2) a) b) c) d) 7

3)a)y =5 —3 b)y=5"% )57 d)y=5254+1 4) a) vertical compression by a factor of % b) horizontal compression by a factor of % c) vertical reflection (reflection in the x-axis) d) horizontal reflection (reflection in the y-axis) and horizontal compression by a factor of % 5)a)y=—7* b)y=3(7%) ¢)y=7i d)y=7(7"%) N 7) 6) r"&( 12T rﬂﬂ"( “542-1)-% Y=y \ - J Xz-3 L‘l J20M . al 8) a) y = 3%*; horizontal compression of the graph of y = 3* by a factor of % b)y= 81§Jr ; horizontal stretch of the graph of y = 81* by a factor of 2 1) Describe the transformations that map the function y = 2* onto each of the following functions... D =ard b) y = 2**3 )y =4 d)y =321 +1 ¢ - R —_ P ALK : - l.'\ - Qo ,'—‘ AT & I\/ O\ .—:‘x = \"71 S VNS -3 A - Rrdyteer Sreyh 5(333'? \Z‘\' horrene) - P "_‘;‘\‘:T 1 () Conpre <A 0N - 1 ( by. \ \\I bave 3 (%) i 2) Create a sketch of each graph for each equation in question 1. (a table of values may help)

b) a)

| , < = | | | 2 " \ \\ = ¢ /'r‘" | - " \_)«\ = e | ) \ -\ L O\ LD | \ | Qe3> -0).* Q.5 ‘_,l \‘ 0. [ ‘. Y 5 -1 \ ° [ “f -~ 3) Write the equation for the function that results from each transformation applied to the base function y = 5%, a) translate down 3 units X b ) \S/ - -j.y ¢) translate left% unit . J'TK* L:‘,.V;- - K N -~ - d) _I’\\ v | / ' ./ i / | v4 | A t 4 v i » <.l » -t = == = 4 S N S - — \ i | /x*- \ \ \ - l‘.‘z" ] | \."( L_," Q 1 ’) \ \{ p 7 \ fa b) shift right 2 units \3’- 2- 3 d) shift up 1 unit and left 2.5 units 0= S v2.5 +\ L

4) Describe the transformations that map the function y = 8* onto each function. 1 , a)y = (;)8* b) y = 8% | VOV Ca) comgre 451 ¢ £ O\ - NOrerta) Comprt 433 A bova - \ [ =) \ b L2 ) c)y=-8* d)y=8% - URsrrreed RV o, ‘(.\\ - \nox T2onYO) Conmf it be 3 5) Write the equation for the function that results from each transformation applied to the base function y=7* a) reflect in the x-axis (vertical reflection) b) stretch vertically by a factor of 3 V) -] A. \A = =Y . A . S An, n ) stretch horizontally by a factor of 2.4 d) reflect in the y-axis and ep=amepss vertically by bafo 7 Cj J ——

7) Sketch the graph of y = 37%5%~1 — 5 by using y = 3* as the base and applying transformations. — O« ‘:‘\ '1*:1\ \A| " ‘; - L J - X | ) - | Yo I/’,_T, - e Vi q q B l\q (7 s 1 | - 4.4% C_) ‘ O \ \(- ’U—/Z ‘ ] | 7} - 1 | L‘ o ‘,’ - L‘ ll\ - A:-l ) | &‘ - () | (“- b LA N 111 Pt~ 8) a) Rewrite y = 9* using a base of é Describe how you can graph this function by transforming the graph of y = 3%, )'4 \ horfzomo) Compression ba¥o 3 b) Rewrite y = 9* using a base of 81. Describe how you can graph this function by transforming the graph of y = 81%, y- 4 /'r ‘\OrQa/\;‘a\.) g‘heﬂ'd\ EOY’C) ?\ 10