Pre-Calculus Review for Unit 2: Functions & Graphs Date: llldtt Kqto Rez i eut FG1 I can understand that a function from one set (domain) to another set (range) assigns to each element of the domain exactly one element of the range. (determine functionality) 1. Which of the following is nof a function given that x is an independent variable? ^ ,-l' . t- tr-, rii ^ -: , a a\ 1 - -\-r 3olve $or "1 ig]) I = 4"1i, x > 0 (t_., i(-2,s),(- 5,2\,{-1,5)} x_t_ 1t, i6l), =4x2+1 6ffi -- gecu)se "$=';', ry=1r1r 2. Determine the domain of the function. Y='/F?+3 J\ ue{ \ave X *'t Z O btca,use* Cal^* 'l,a Le 'f + 4 N o?a N€X , {vtaY\bet ! x r4 \on,.uo^ld n<e/ a l"o nna-t x re s*'rh-# t a rt, l2l bOona,,-rr j-S----}- z-L 3. Use the Vertical Line Test to determine which graph defines a function. r3r k_ -.10::: 1l++-*-r* :": : :lp 111--::2 :::x :.: lenYt ca} Iinn, .r ,an1 S,r^6h ott \DY Q^r c'V On'
Transcript
Pre-Calculus Review for Unit 2: Functions & Graphs
Date: llldtt Kqto Rez i eut
FG1 I can understand that a function from one set (domain) to another set (range) assigns to eachelement of the domain exactly one element of the range. (determine functionality)
1. Which of the following is nof a function given that x is an independent variable? ^,-l' . t- tr-, rii ^ -: , a a\ 1 - -\-r 3olve $or "1ig]) I = 4"1i, x > 0 (t_., i(-2,s),(- 5,2\,{-1,5)} x_t_ 1t,i6l), =4x2+1 6ffi -- gecu)se "$=';',
ry=1r1r2. Determine the domain of the function.
Y='/F?+3J\ ue{ \ave X *'t Z O btca,use* Cal^* 'l,a Le 'f
+ 4 N o?a N€X , {vtaY\bet !x r4
\on,.uo^ld n<e/ al"o nna-t x re s*'rh-# t a rt,
l2l bOona,,-rr j-S----}- z-L
3. Use the Vertical Line Test to determine which graph defines a function. r3r k_
-.10:::1l++-*-r*
:":: :lp111--::2
:::x
:.:
lenYt ca} Iinn,.r
,an1 S,r^6h ott
\DY Q^r c'V On'
FG2 I can use function notation, evaluate functions for values,'arld interpret statements that usefunction notation in terms of a context.
Find the indicated values of the function.
. O) {Q)' 3 rX C'|Yt t =J+t(.tt")l--r if x<4I z* "^-,- =3+l2t[3+Bx'ilx>4 =l3l
b /(o) t) +(o) = -| to)d f{44) -_ D
4. Iu) =
o) f (e) = -* (z), =E: or't,S
D f <q,Y) = 3+t tq,q)z,,, ,,=.3-#g (1,?,36)
=J,*t54ZY= 15-7,76a.f{4)
c /(3)
5. -{t*) =[x]- 3x
a. /(s.3)c. /(0.t)
b. /(- 4.6)
o) 9(E,a) = [5sl' - t(s3)
t4I
t5I
=
t) X-'l,t )
c) t(r,, t) =
5 - t5,?-lO,q
= tq,u7 -3(4,b>
= -5 + lv,$= U,g
[u,tl -3(b,l)l, 18,3
-1Q,3
Crrr^*el.* Ltegor[rrr.,c-]ron rcu-'nda
t*J
+z {4^-0,0194r,,o 'W
FG3 I can analyze graphs to find dornain, range, local maxima and minima, inflection points, andintervals of increasing, decreasing, concave up and concave down.
6. Find the approximate intervals on which the graph of /(xi = - *{, is concave up and those
on which it is concave down, and estirnate all inflection points.
-.n1,' "on"ave downward
[- *, - 3)
,ro [:,-} concave upward (- 3 :)points of inflection at - 3
,* 3
L@i) .on"ave downward [-: 3) concave upward [-
*,, -:) ""0 [3,*),points of inflection at - 3
-.0 3
@"ncavedownward( * 3) i.(3
-) concaveupwardt-3 3ipoints of inflection at - i ,"0
3
(in-i) non* or these
4.4[n "-tJ..-,
Cal u,t-talon.+a
A ^rt *4e into,rwls\o^ ^"^1
need 4-u
:h -in ,L*l-a 5o"risI uscd a u,,;rtdew
hJ i +4^ ! -rr.4n otle *d 1-mora*D,5 ,
S |'"+t\..'
Find all local maxima and minima and points of inflection of the function
.f 1x7 = -2x3 - 6x2 + 18r - 6.
r = -3 is a local minimum, r = 1 is a local maximum, x= -1 is a point of inflection.
r = 1 is a local minimum, r = -3 is a local rnaximum. x = 0 is a point of inflection.
r = -3 andx = 1 are local maxima, r = -1 is a point of inflection.
r = -3 andx = 1 are local minima., x =0 is a point of inflection.
S lte la[' Y--3.sa lrca-l fyr-in,
X=l isa loco.[ r^ax
Poln* oQ \.r$\ec+1 0n I X=-l
-3+t - **=-\.2&
*
[3 ;{,0)
L The graph below defines a function /. Determine the following:a f(-2) = 2-b /(1) : 6>
c. the domain af .f -Ll<X4^5d.theranseot f -3<5a3
', PrrriLb'{s
Do""ein ', ?oss;ble y' s I8l &e a bo ve,
FG4 I can write quadratic functions in different but equivalent forms to find the vertex, findintercepts, and sketch a graph.
9. Determine the x-intercepts and the vertex of the graph of the quadratic function F
"f{r)=x2+9x+20.
i[n]i fne x-intercepts are -4 and *5.verrex is (a.5, 40.25).
i[B]) The x-intercepts are 5 and 4.
To $nd v$+a4 '
] ?'*-'ao
l[C],. Thex-intercepts are 5 and 4.Vertex is (-4.5, -0.25).
kffif
19] D
I (x)-- Yz+ Qx +zo
$tx)= (Y'\qx)'+?'b+20'25,- 2a75
+ lx) = &t''-' x lb|*) -,2{tx) = (x *
'1, 5)z -,2y<rtlr,x (_1,5,
f(x) = Yz+4x+e-o
f ix) = 6( + 5)(* "u)' o= (Y+E)d +Ll)X+ 9=o X+4:D
Y: *5 X= -{
?vur \le \ n Ver$ qt (++r-^5f".r^o*t oa){a r-vvt ,
Cf -- (/'5)'= Lo'z$'='
Aad)y r'^A s"bt*&"X is eX+tivelo*f5 .la od.l )n4 0, , -b x'*[x'*"Ll.u *a']ons as (x + |'trt
-,25> Dh*You
^' ' (x-in*) L^ l- N -r 5a'ta'rtd
zo F I ,\d, 'zenos , 3 ol ,n b y |a clq e'kf' *'r 'oa QuaMoJAc +o{'""ru*M;
t'5
?"* { r- c so sa\v<'
Y-t,*l<r"<f+5 oJre - 4 "^ d -5 '
(ioi) rn" x-intercepts are -4 and -5.Vertex is (- 4.5, - O.ZS)
10. Determine the vertex and y-intercept of .ttte function,and qketch a graph,
V*lor* is L-1,2>t5-irl.*2,^o.4+ i='^lkc-^ )(= D
{to) = J(o+ Dz tz= 3(r)-*z
-_ jrZel^€ J
(o,5)
11. Which is the function .ft*) = x2 +14x + 57 in transformation form?
i@ f(,) = (r + 7)'' 8 (fCl.) /(4 = (r + 14)2 + 15
f (x),
$(x) r
l(^x) =
110l
r11t D.
(ng rtrl=(.r+14)'z- 1s d. =,rhlto* ef
I )4\z - '12 =(zl ,
*b1 3PtI+DgSa c*or a s
Xt+ ),1 y + 51
(^"r )'lx )-4f u
(x +-r)'+ f,
,rq
l*z(x*
{.erna su*2/
{a
FGs I can identify the effect on a parentfunction of transformations for speeific values of k.
12. Find the rule and the graph of the function whose graph can be obtained by performing thetranslation 4 units right and 2 units down on the parent function .f l*) = x'.
13. Findrthe'rule and the gxaph efthe function,rrhose'graph,eqn be obtained'blr perfsrmingdhe
translation 2 units left'and 4 units,uP,an"the'parent function /'(*) =i* | ,, r ',:, : ., '
,1rni)rt,l=|,-zl+a (Ci; rt.),=lx+21-4,, : ,
ilDlri none of thege
14. Find the rule and the graph of the function whose graph cap be obtained by performing'thetranslation 4 units left and 2 units down on the parent function /(r) = ru.
(1n1) r(,) = (r + 4)3 ;) ilDl i none of these'.-. -:
,
|tx): x 3
(D 4,".,J*s l($t,*(x)*_ (x * q)=
@ 2,,u,'j*s dourt
I r-r<)= (x t',)=- a
r14r EFG6 I can ccmbine functians using basic operations (*, -, x, l) and compose functions.
15. Let /{r) =1-x2,g(r) =1-{. Find {/ug;1r) and itsdomain.
l15l *x"-v +Zb arr."aj.rr-:
*b-rudruu-aL+-a
16. Let./(xi = 16*r', g{r) *4-x. Find t/-SX") and itsdomain.
(tt -:c.(,t-x)-Yz+?t+ Ia bo*'j'-^ ; R
17. Given /(") = x3 and dr) = - 6 - 5x, find {S' " .f){"} and its domain. t171 A,._l:'. -6- 5xr[C]) "-:, r+0..-____r' X"
ifnt) non* of these
1(x') = -b- 5x3
,f C lsR- a,-d, X
r: E ga dA'rn^;
1161-/z+y+ leb"rrra,ivr I
a!..[ n o-a0 nn tr-^n-lrer,r
,,t!_1) -6 - sx, .r: *
3(€cx)):
\, "r.;-"
t62l--Xs
ilIii::J. ::
,€ L1'+}x) it R-
FG
18.
7 I can find an inverse of a function and verify by camposition that functions €re inverses.
4x+8g
w,t
Find the inverse of the function.
J\x)= 4 .t=I18] A
\p,t^:rif e.€.&) as \t5r^.r\ \ cL X *d X.
4x-8
't 3o\ve Crs. *n\-
{x= 1q-B \)
J
1tx)=tl**t ry=;.rLdr'r-tr^sx(x},19. The graph of a function f is illustrated below. Which is'the graph of the inverse function of ff
='i,s* = #QlnW*) -* 35?--tD = 1.L? {at {lirdz},ff .6 E.-l- r_Jlqjr", lo T- -*-{*1*--,.::_:-'.,ZZ. 'inegraph shows the weekly amount of sales(in tnousanild*Ot dollSr$ made by a company over
a period of ten weeks. Estimate the average rate of change of sales (in dollars per week) over
f",i:'r interYals
^\s ,, D $ (8 - 9c t) '2'bnt-t4<'a\) " Ia. 1toS
23. For the function l'(r) = 3x2 *7r +6, find
a. the difference quotient.b. the average rate of change over the interval 1 to 3.
