QuestionQuestion

Transcribed TextTranscribed Text

(1 point) The graph of y = x is given below: Find a fonnula for each of the transformatio ns whose graphs are given below. Recall that absoluta value is enterad as abs. a) y = b) y = •• (1 polnt) FORMULAF ROMS QRTG RAPH The graph shown Is a shlft, also callad a translatlon, of y a= ±lor ±2. - -,'- - -,'- - ,' - - ,' - - 'r - - 'r - -,'- - -,'- - ,-' - · ·1 O 1 • L .. .,1,. • .,1 .,. ., -,- .. , .. - '1 - - " - - .. - - I" - .. , .. - .. , .. - "1 - - ' -4 The graph Is y r 2 ' ' ' ' .... • .... L .... • .... '' '' '' ' • • • • ' ' 1' 'r ' i o ,' . -_, - .. --~ ----- - -.. _,_ - ' ' ' ' ' 1 1 1 1 1 --~--,--r-,--,- --,-- - - r' - -,'- - ... ~ .... i .... L .. J .... 1 ........ ~ .... L .. J .... 1 .... 1 .... ' ---·--·--~-4--·----·--~-4--·--~- ---,'1 -- --,1' - ',1 -------,--,'1 11 - t, --,-'1 -,-1!- -1 2 Find the formula tor f. f (x) = ±Jax, where - - ~- - _,_ - _,_ - -~ - - ' ' ' ' - - .l. - - -' - - .J_ - _,_ - _,_ - -L - - '- - - ' ' - - .1 - - .J - - J_ - -'- - -'- - -L- - L - - 1 1 __ ·- __ , ___ , __ - ·- ' 1 t 1 1 ' 1 1 t 1 1 - - , - - -¡ - - ,- - -,- - -,- - ' ' ' - - "T - - ., - - ..,- - -,- - -, ' 8 - - ~- - _,_ - _,_ - -~ - - ' ' ' ' - - .l. - - -' - - .J_ - _,_ - _,_ - -L - - '- - - ' ' - - .1 - - .J - - J_ - -'- - -'- - -L- - L - - ' ' 1 , __ • ___ , ___ , ___ • __ , 1 1 t 1 1 t 1 ' ' 1 1 t 1 1 ' 1 - - -¡ - - -¡ - - ,- - -,- - -,- - -, - - ¡- - - t' 1 1 I - - -r - - , - - -.- - -,- - -,- - -r- - r- - - 1 1 1 1 1 - - -r - - ., - - ..,- - -,- - -,- - -r - - r- - - -8 ~--.J __ J ' ___ , ___ , ___ 'L --L- ' _, - - _,_ - 1 ' ' ' ' -'---'--- '' '' I t I I t -¡ - - -,- - -,- - -,- - - ' - ' ' ' -,' - - -,1- - - r' - - r' - -, - - - ,- - - r- - - r - .l.---'--~---·---·---~--'-- ~--.J __ J ' __ J ' ___ , ___ 'L --L- ' ' < 1 _, ___ • __ 1 _, ___ .___ 1 I t 1 ' ' '' '' 1 I ' 1 I I -¡ - - -¡ - - -,- - -,- - -,- - - • - ' ' ~--,--,--~--' -,---r, --r- 1 ' • ---r---,--,--' -,---,---r---r- - 1 - 1 - 1 - 1 - 1 - 1 - 1 The domain of g( x) is of the form [ a, b], where a is and bis The ranga of g ( x) Is of the form [ e, d], where e Is and d Is Enter the letter of the graph which corresponds to each new function defined below: 1. g(x - 2) + 2 is 2. g(2x) is 3. 2 + g(-x) is - 4. g(x + 2) - 2 is A B e D {V\ E F G H (1 point) The graph of y = f (X) is given below: 2.1 A(• ,O) CI ,O) x On a piece of papar sketch the graph of y = f ( X - 5) and determine the new coordi nates of points A, B and c. A= B= C= On a piece of papar sketch the graph of y = - f ( x) + 2 and determine the new coordi nates of points A, B and c. A= B= C= (1 point) The graph of y = f (X) is given below: y B 21 A(· ,O) C( ,O) X On a piece of papar sket ch the graph of y = f (!X) and determine the new coord inates of points A, B and c. A ( B( C ( ) ) ) (1 polnt) The graph of y = f ( x) is given below: 2.1 A(-1,0) C( ,O) X On a piece of paper sketch the graph of y = -4 f ( 6x) and determine the new coordlnates of polnts A, B and C. A ( ---~ ~--- ) B ( ) C ( ) (1 point) Given f (X) = 1 X 1, after performing the following transformations: shift to the left 14 units, shrirnk vertically by a factor of / 1, and shift downward 65 units , the new function g (X) = Use abs(x) for IX1- (1 point) The graph of y = x3 - 12x2 is given below: Find a tonn ula tor the transfonnation whose graph is given below. y= (1 point) The graph of y = f (X) is given below: y B 21 A(• ,O) C( ,O) X On a piece of papar sketch the graph of y = f ( X - 2) and determine the new coordi nates of points A, B and c. A= B= C= On a piece of papar sketch the graph of y = - f (X) - 1 and determine the new coordi nates of points A, B and c. A= B= C= e o E 8 -4 For each equatlo n, enter the letter of the corresponding graph. y= J(x - 4) y= -f (x + 4) y = 2f (x + 6) y = J(x) + 3 y = ~f(x) (1 polnt) The graph of J.J . ' x2 Is -5 lven below : . -. - ' . . ' ' . ' .' ..- - - - .' .- - - - . ' • .' Find a formula for the transformation whose graph is given below . -.-----.-----.-----.----- ' -.-----.-----.-----.----- ' -.-----.-----.-----.----- ' e ---.-----.-----.-----.----- ' -.-----.-----.-----.----- ' -.-----.-----.-----.----- ' -.-----.-----.-----.----- ' -.-----.-----.-----.----- ' -5 y (1p olnt)C onsldethre f unctlons (1 polntC) onsldethre f uncllons f(x) = - 5x + 9,g(x) = 8x + 1 f(x) = 3X,g(x) = x3 Determitnhee f ollowlngc ompollslons off unctlonsD: etermitnhee f ollowlncgo mpollslonso ff unclotns: (fof)(x)= (fof)(x)= (fo g)(x) = (fo g)(x) = (g o f)(x) = (g o f)(x) = (g o g)(x) = (g o g)(x) = 1 (1 polnt) Let f (X) = x 2 + 5, g (X) = -- , and h( X) = v'2x . Flnd a x- 2 formula for g(f(h(x))) = (......_1 ____ ____,] (1 point) Consider the function g (X) representad by the table below: X -6 -4 -2 0 2 4 f g(x) o 6 -64- 2 -42 Comp lete the tab le of values for the INVERSE, g- L x , In the tab le below: ~ 4 -2 O 2 4 6 -2 (1 point) Decompose the function below into u ( v (X)). In each part, basad on the tunct ion v( x) given, tind the correspond ing u( x) needed to decompose the tunct ion. 3 +x2 y = 8 + x 2 (a)v(x) = x2,u(x) = (b) v (x) = x2 + 3, u(x) = (1 point) ldentify the function f (X) if k(x) = (J (x))4 = cos4 (6x). f (x) = (1 point) ldentify the funct ion f ( x) if j(x) = ,/J[zj = J e (x2 +1)_ f( x) = (1 point) Use graph below to calc ulate the following: (a) f(f(2)) = (b) g(g(2)) = (e) f(g(l)) = (d) g(f(l)) = Í (IC) • • (1 point) Use the table of values for the functions p( X) and q( X) below to comp lete the tables for the compos ite functions defined in parts (a) and (b): X 012345 p(x) 2 1 053 4 q( x) 52340 1 (a) comp lete the table of values torth e composite funct ion r( x) = p(q (x )) at X = 0, 1,2, 3,4, 5 o 1 2 3 4 5 (b) Complete the table of values for the compos ite function s( X) = q(p( X)) at X = 0, 1,2, 3,4, 5. o 1 2 3 4 5 (1 point) Decompose the functio n below into u ( v ( x) ). In each part, basad on the functlon v( x) glven, flnd the correspondlng u( x) needed to decompose the function. (a)v(:i;) = x5, u(x) = (b) v(x) = x5 + 5, u(x) = 5 +x5 y= 8 +x 5 (1 point) (a) Use the tab le of values for f (X) and the graph given for g (X) to calculate each of the following: Qf(g(5)) = ii)g(J(5)) = -=i iii) f (f(O)) = ivJ g(g(O)) = (b)g(g(x)) = l whenx = 5 4 3 X 012345 J(x) 34052 1 ---"--------J--------'---'- ---- g(x) - - - - - -1- - - - - - - - - _,_ - - - - - - - 4 - - - - - - - J - - - - - - - _,_ - - - 1 1 1 1 2 3 4 ' (1 polnt) Suppose J(x) = -:i; 2 + 9x - 18. (a) For which values of X is the fu nction f (X) positiva? Enter your answer using lnequallt les. help (lnequallt ies) (a) For which values of X is the fu nction f (X) negativa? Enter your answer using lnequallt les. help (lnequallties) (1 point) The concentr ation of a drug t seconds aft er injecti on is given by C(t) = 9t + 1 5t2 + 3 Graph this funct ion on your calculator. Estímate the time at which the concentrat ion is highest (your answer needs to be correct to at least one place past the dec imal point): Maximum is at t =

Solution PreviewSolution Preview

These solutions may offer step-by-step problem-solving explanations or good writing examples that include modern styles of formatting and construction of bibliographies out of text citations and references. Students may use these solutions for personal skill-building and practice. Unethical use is strictly forbidden.

    By purchasing this solution you'll be able to access the following files:
    Solution.pdf.

    $75.00
    for this solution

    PayPal, G Pay, ApplePay, Amazon Pay, and all major credit cards accepted.

    Find A Tutor

    View available Mathematics - Other Tutors

    Get College Homework Help.

    Are you sure you don't want to upload any files?

    Fast tutor response requires as much info as possible.

    Decision:
    Upload a file
    Continue without uploading

    SUBMIT YOUR HOMEWORK
    We couldn't find that subject.
    Please select the best match from the list below.

    We'll send you an email right away. If it's not in your inbox, check your spam folder.

    • 1
    • 2
    • 3
    Live Chats