Power Functions/Polynomials Test ReviewPower Function Inverses -K~Find the inverse of each function algebraically. (Youwill be asked to do this on the test J

WITHOUT a calculator)

1. y ~ 2,Jx+4 -3 ~yC:3:)':'\i 2. y ~ 2 x~ +5 lj :.@lkS~3x.~-:3 3

3. Y = 5(X_~~ 4. Y = 'tlx-1-4

'::)=±~ ~ ,&. 3 j = (x+l..\)'''' I;)(. "!. - Y.Solving Power Equations

Solve for x. Check for extraneous solutions. (Youwill be asked to do this on the test WITHOUTa calculator)

1. VX -9 =-1)(.,~c:; \2.

5

3. (x + 3)2 = 32X:. l

2. .Jx+25 = 4}(.,:-q3

4. (X+2)4 -1 = 7X. ::. I Lot

6. ~x+4 = ~3x-2X.=3

9. 5.Jx-1 = .Jx+1

)<.= ~1'2..

5. ~2x+6 = 2X=S

1 ' ~8. 4 (7x + 8)2 = 54

X-:Lt(Youwill be allowed to use a calculator on word problems)

7. x-lO = .J9xX: 2..5

3

lO. The length / in inches of a standard nail can be modeled by / = (54d)4 where d is thediameter in inches of the nail. What is the diameter of a standard nail that is 3 inches long?

O.OcgO ',nches

11. The formula t = ~ dZ

gives the time, t, in hours that a storm with diameter, dmiles, will last.216 • \

If the storm lasts 2.5 hours, find the diameter of the storm~ ~:-r 42.. VV\ \ et5

12. Find a value of kfor which ~x + 1+ k = 0 will have no solution. Justify your answer.t<>O

13. A Plasma TV has a rectangular screen. The width of the screen is 33.1 inches and the lengthis 22.5 inches. Find the length of the diagonal of the TV to the nearest inch. 1..\0 'W\clt\es

14. One version of the lawof tensions from the study of sound is 1i = fz rK. If Fl = 250,VlfFz = 30, and fz = 265, find fl to the nearest hundredth. "(p4.q~

15. Einstein developed the formula E =mc2• In other words, the amount of energy released, E, isthe mass of the object times the constant, m, for the speed of light squared, c. Solve forthe speed of light. Leave your answer in radical form. _!

~- -lIY\

Power Functions/Polynomials Test ReviewPolynomial CharacteristicsFind the x-intercepts, y-intercept, end behavior, and multiplicity of each root. (Youwill be askedto do this on the test WITHOUT a calculator)

1. f(x) = x3(x + 2)(x - 8)2

x: (0,0),( -2,0),(8,0)

y: (0,0)(8,0) has multiplicity of 2

(0,0) has multiplicity of 3

even degree polynomial,positive lead coefficient

{

X ~ -oo,y ~ 00

x ~oo,y ~oo

x: (0,0),( -2,0),(2,0)

y:(O,O)no multiplicityodd degree polynomial,positive lead coefficient

{

X ~ -oo,y ~-oo

x ~ oo,y ~oo

3. y = - 3(x + 2)2(X -1)4(x - 3)3

x: (-2,0),(1,0),(3,0)

y: (0,324)(-2,0) has multiplicity of 2

(1,0) has multiplicity of 4

(3,0) has multiplicity of 3

odd degree polynomial,negative lead coefficient

{

X ~ -oo,y ~ 00

x~oo,y~-oo

4. The x-intercepts of a polynomialfunction are (2, 0), (0, 0), and (-1,0) which has a multiplicityof 3. The leading coefficient is negative.a. Write an equation in factored form for this polynomial.

«:1 = -}((X-l.)(x.+ \)3b. Find the end behavior and the y-intercept. ~}{ ~ - CO lJ\~ 0()

~-\Y\-\- (OtO) l~ ~QIO ~~-ooFind the x-intercepts, y-intercept, end behavior, and multiplicity'oPeach root. Then make asketch of each graph.

9. x-intercepts: (-1,0., (3, O. has a multiplicity of 2, (0, O. has a multiplicity of 2;end behavior: {X ~ - 00, y ~ - 00 t.l:" '2.(x. ..• ,)(x._3)2-

x~oo,y~oo 0

a) {X~-oo,y~oo

10. y-intercept: (0, -4 ; end behavior: ; ~(~ ( )2.x-intercepts: (-4,0.; (3,0.; (2,0) has e:;m:I~;;tY ~ ~()( .• '-\ x, -~ X ...2

Power Functions/Polynomials Test ReviewSynthetic DivisionFactor the following. (Youwill be asked to do this on the test WITHOUT a calculator)

1. X3 - 5x2 - X + 5

l~-t-l)(x-S)(X -I)3. x3 _2X2 -5x+6

(X - 3)(X - ex x +2)5. 3x3 + lOx2 - x -12

0l+ ~)(x-I)(3x+Ll)Solving PolynomialsSolve the following for x by factoring. (Youwill be asked to do this on the test WITHOUT acalculator - you will be allowed a calculator on word problems)

2. x3 -12x+16 2()( fLt)(X.- 2.)

4. x3 _X2 -6x

X. (X.-3)(X.+ 2)6. x3 -18x+27

()(.-.3)lX.2-1-3)<. -l1')

1. x3 - X2 -18x -18 = 0

)l = -3, x = '2-t-..{lc;, ><.= '2-~2. x3 -l1x2 = -24x

3. x3 - 3x2 - 5x + 7 = 0

X= I, 'A. = I+2-fl' X:.IO.fx=-2

5. x4-4x3-lOx2+17x=-22)(..-:. -', X. :: 2 X = -3+~ x.= 3-...rs3'

, 2.) 2-7. X4 +3x3 -3x2 -l1x = 6

6. x3 -8 = 0

'" = 2. ~ - - \ +-L '3 X = -l- ~€l -- ~~,

8.x5-4x4-2x3+4x2+x=Ox,= -( }(:O K= ,

X. = 2+€ x. = 2.-€9. The volume of a giant sequoia can be modeled by the function

V = 0.485h3 - 362h2+ 89889h - 7379874. The height of the tree, h, is measured in feet andis restricted to 220 s h ~ 280. (calculator use allowed.a. What is the height of a tree that has a volumeof 42,250 cubic feet? 113.4:;' If+b. The LincolnTree in the Giant Forest in Sequoia National Park has a volumeof 44,471

cubic feet. What are its possible heights? 2lJ..t,Q l-3f+ 0( 2.(pr.43lf ftc. The actual height of the Lincolntree is 255.8 feet. What is the difference between the

true volume of the tree and the volumegiven by the model?

\It\e ~\ VO\ume \~ \11. ,qq {2+3'llr~f-+hm #-e volume at ~ ht\odel

)(.= - () x::. -3J X = 2