MIT Academy Period:Algebra 2 Name:

Chapter 6 Assessment Complete these problem to make sure that you are prepared for the test.

1. Ifj(x) = 2x3+7 and g(x) = -3(x -9), find the value of each expression below.

= -5~j.t3

00 . 3,e

e.) Aref(x) and g(x) inverses of each other? Justi~’

W~

6x2—x—2

x2—4x—2V

if X -21

~.A~

a.)jt-3) ~ 2tt3)h43

1~ytc.)f(g(-3)) /

b.)g(-3)

t _3(’~~,,) ~427

ck€J

t±, ~~scra

~

your answer

c~~)) s~et-tdr’3 ._tj

— 4x + 3b.) x2—9

KCF~‘2 ‘j,( 43 _________

)C~~ ‘1

r

2. Simpli~’ the following expressions:

a)C-4~j XYXY8x3 4x2y

r

1C~

Af

4 ~2

~%2J1$13~(~~

•, ~t;

314-’ I(~A

~k{eVc

a

Algebra 2MIT Academy3. Subtract and simpli~’ the following expressions:

x—2 x—4a.) ~ — x —3

I x—1 x+Ib.) 2 ÷ x2+2x—3 — 2x+6

I (~Y,cj) —

jt3 2-26ck3) )6JY)2&.3) ____

_F~ I)tt3-42-Xj .1- -

= 26fl) ___

.

5. Graph on àometric graph paper

) .—i~

j..t; (2~≠t9) -3~

6~ 2t~2o$

Sx1,20A1& /

a. Sketch a graph of the solution to the equation: 4x ÷ 6y÷ 3z = 24.~.•.•.•.•.•

• . • . . . • -lit

•:•:•.•.•:• ••:•:•:•:•:~:•:•:•:~:• :•:•:•:•:•: .t.~t3±.!~°• : • : • : : : : : • : •

:~:•:~ :~: •: :• :~ :• : • : • : • : • : • : • : • : • ,~ y:rf.C:.:::.:::t~__~~___

• ~

-3r-2’l(ero-Ø)-

b. Graph the point (2,3,5). What are three otherpoints that have the safiuiisometric d~t position?

6, ‘.~)(C) L1 i)

.

Itzt ~,

4,2(’9~)

Name:Period:

~tCD

~2 4j_15

4-~c’ -20) ~&t3)

4. Identify the vertex and thejine of s mmetry: f(x) = 5x2 + 20x — 16

~

~Øj~

•p 4’):

*J .r~ yecies: (—2, -36)lute 0ç 7$4M4~O( =-

.

• •

U,,

.1 4~ €~( -$~

lest/toe ,h0~,A’

Nc4ke~ s.J4~ty ~? 2/ Name:/ Period:

!~?jfl: iC

7. Solve each equation below for x

_1 tq,,)~3b~s:2 t—(~43b5

j —23 t 3b

Algebra2 LØLIA?? -4, Vnplruc’<Mil’ Academy6. Solve for x, y, an~he system of equations at below.

— 2y + 3z = 32x+y+5z=8

3x — y — 3z =

3cc_L?~

/AU ~1~4d~oi~ -‘

cnce( ~_1. v’ar~We

Sc)”

c~x~4 iq~g

~3zr~fl

~5’ ~27t44

5x.2t .~ -.-f4L

..t ~3~z.tfl

_IIz:33

42(3):: -pi

:a=3

(-‘i) 28

4~~

.gflz3

.34)23

= 3ge3a. 18 = 2(3)(x+3) b. 128 = 43X

3$

I, 21 ~~7KI’

7~C≠ ~t,L__ ~~73

pg

by’ P6

06

_3P

•, ~El.-34 —c’8 What f~ the equation of the parabola passing through the points (3, 1), (2, 3), and (0, —5)?

~KQ1ACA

~‘$ ~~ezy~sbXtC

~~4’~3~)4c ~_,J~7~~3b 4C IrTa43b-5 —v

—? e=-S j1Rt3b~,a4~,YtbS)1C _73zt4~÷2b-fC —(2 ~a

42 —in-—-p 12-ia..’

“—p k42b3.2~4Q)

34

—1 —t—P —D 2xr •13

11. Find the inverse of each of the functions below. Write your answers in function notation.

a)p(x)~(x+4)2+1

2)(~

2(y-O ~4q)

I,

X~ 34~d7’’

-2

&

Algebra 2 Name:MIT Academy Period:9. In parts (a) through (b), rewrite each expression as a single logarithm. In parts (c) through (f), solve each equation.

a. log2(30x)-1 log2(6) ..rtt,, 4 (2$~) —si

b. 21o~(x)+log3(5) ~, hy3X’~~;~ ~$36x2

c. log7(3x—2)2 —.D 72~3(~2 -~ qy~ 3~-2 —) hg9 3~ —t

d. Iog(2x+1)=—1 —a ~

e. log5(3y) + logs(9) = logs(405) —‘ 275 2?y 4;#cfl ‘~ç4~ =4O~ ~-, ~, :15

f. log(x)+log(x+21)2 —v 2 —w ~ rP

~ ~

10. Find the equation of the exponential functi~asses through the points (2,264) and (6, 4044) and has a horizontal

uYtOl. ,

asymptote at y = 12. (hint: think about 6.2.3 and use y = ab’ + c.

C:)2

2≤~ta.h~t12

a52:ct~b’ 1%

252rO~ ___

r tjO3Jt26) W~’z52

(Ezr1~

.

b.) k(x) = 31og2(x —2)

I-It2)

y

MIT Academy Period:Algebra 2 Name:

12. Define the vocabulary. You may use words, examples, pictures, symbols to convey what you mean.

Logarithm:

Power property of logs:

Asymptote:

X-intercepts:

Plane (in the context of algebra 2):

yc-(.6 Asd ycif’

b eRi~ catet *i~oo+ < - ~

e. Solve and show the solution on a number line: 1x + 3 <x2 — 2x — 3.

)E:~t7 e7.5,2~)t_d

a line, one is a parabola {extra credit if you complete the

y

‘1,5)

square to put it into y = a(x — h)2 + k})13. Graph the system: (hint: one of them is(‘0,3)

y=~x+3 ~kpe~fr~°~

y = x2 — 2x —3

I

b. Use the graph to solve + 3 = x2 — 2x —3.

rtJ

O ~

O’

t@7 (~)-3

-3-I

~o)

(~,-3)

~c.Solvey = __________

d. What is the difference between the answer to$andt Explain why this is so.

liD’,

4frre ;~,4ke

—‘.5

$t3

‘Vbeio~o44e b/k~4 01g~

Ar% y4-15

Name:Algebra 2MIT Academy Period:

For problems f and g, solve by shading the appropriate region.

i.y≤~x+3

y ≤ x2 — 2x — 3

j.y≥~x+3 k.y≥~x±3

y≥x2—2x—~ y≤x2—2x—3

(/7.it/ /~c //7

Jl////li ~

~,4 7,/f

h. y — 2x —3

y ≥ + 3 a6qre

.

.42w1Q ce

S.

/1’

/I’

/

/L