ALGEBRA II CHAPTER 7 NOTES. Name

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1 ALGEBRA II CHAPTER 7 NOTES Ne

3 Algebr II 7. th Roots d Rtiol Expoets Tody I evlutig th roots of rel ubers usig both rdicl d rtiol expoet ottio. I successful tody whe I c evlute th roots. It is iportt for e to kow/do this becuse th roots re used i solvig rel-life probles. exples: x x rdicl d frctio for. x x x x x. x power root Do the root first the the power If is odd, the hs ONE rel th root: ex: If is eve d 0, the hs TWO rel th roots: If is eve or odd d 0, the hs oe th roots: If is eve d 0, the hs o rel th roots. ex: 7 7 or ex: DNE 6 6 Eve roots hve two swers (oe if the uber is egtive), d odd roots hve oe swer, either positive or egtive

4 .,., 6., x x. 6 x 0. x 6. x 8. x 8. A bsketbll hs volue of bout 6.6 cubic iches. The forul for fidig the volue of bsketbll is pproxitely V.8879r. Fid the rdius of the bsketbll. rdius = 6. The rte r t which iitil deposit P will grow to blce A i t yers with iterest copouded ties yer is give A t by the forul r. Fid r if P = $000, A = $000, t = yers, d =. P r = Hoework: pge 0 -odd, -,7, 9- (do ot use clcultor), -60 iddle colu oly, 6-6

5 Algebr II 7. Properties of Rtiol Expoets Dy Tody I usig properties of rtiol expoets to evlute d siplify expressios. I successful tody whe I c evlute d siplify rtiol expoets. It is iportt for e to kow/do this becuse rtiol expoets re used i solvig rel-life probles. The properties of iteger expoets fro Lesso 6. re lso pplicble to rtiol expoets. Product of Powers: Power of power: 9 / / Power of product: b b Negtive expoet: Quotiet of powers: Power of quotiet: b b / / // / Hoework: pge -, -6, 8, 0,,, 0,,

7 Algebr II 7. Properties of Rtiol Expoets Dy Tody I usig properties of rtiol expoets to evlute d siplify expressios. I successful tody whe I c evlute d siplify rtiol expoets. It is iportt for e to kow/do this becuse rtiol expoets re used i solvig rel-life probles.. 7x. 9 6g h. x y 0. 8rs 6. r t 9 d g h 6. g h x x x x x Hoework: pge 8, 9,,,, 6-6, 68-7, 76-78

9 Algebr II 7. Power Fuctios d Fuctio Opertios Tody I perforig opertios with fuctios icludig power fuctios. I successful tody whe I c perfor opertios with power fuctios. It is iportt for e to kow/do this becuse power fuctios re used i solvig rel-life probles.. Let f x x d g x x.. f x g x b. f x g x c. f g d. g f e. f f. Let f x x d g x x.. f x g x b. g x f x c. f x g x d. g x g x e. f x g x f. g x g x

10 . Let f x x d g x x.. The product of f x d g x b. The quotiet of f x d g x COMPOSITION OF FUNCTIONS COMPOSITE FUNCTIONS f g x or g f x Coposite fuctios re whe oe fuctio is plugged ito other fuctio.. Let f x x d g x x.. f g x b. g f x c. g g x. Let f x x d g x x.. f g x b. g f x c. f f x Hoework: pge 8-0eve (you do ot hve to stte the doi)

11 Algebr II 7. Iverse Fuctios Tody I fidig the iverses of lier d olier fuctios. I successful tody whe I c fid the iverse of fuctio. It is iportt for e to kow/do this becuse iverse fuctios re used i th clsses fter Algebr II. A iverse reltio is reltio i which the iput vlues (x) re switched with the output vlues (y). You switch the x d y vlues. To grph it, switch x d y, the solve the equtio for y.. x 0 6 y - 0 (this is exctly like questios #, i the hoework) x y (these re exctly like questios #6- i the hoework). y x. yx. y x. f x 6x 6. Fid the iverse of y x 6. Grph the origil equtio d the iverse. NOTICE the grph of the origil d the iverse reflect over the digol lie y = x.

12 f x x 7. Here is grph of log with soe of its poits i x-y T-chrt. Sketch grph of the iverse. (this questio is very siilr to questios #- i the hoework) Is the iverse fuctio? YES NO Horizotl Lie Test usig the origil grph, if horizotl lie crosses the grph ore th oce the the iverse will NOT be fuctio. **If you cosider oly prt of the grph of the origil fuctio, the it c hve iverse. For exple, if you were sked to fid the iverse of f x x, x 0. This is clled RESTRICTING THE DOMAIN. (these re exctly like questios #8- i the hoework) f x x Iverse fuctio? YES NO 9. y x f x x Iverse fuctio? YES NO Iverse fuctio? YES NO (this is exctly like questios #8- i the hoework). f x x. f x x, x 0 Hoework: pge 6 -, -, 8-

13 Algebr II 7. Grphig Squre Root Fuctios Dy Tody I grphig squre root fuctios. I successful tody whe I c grph squre root fuctios. It is iportt for e to kow/do this becuse squre root grphs re used to help solve rel-world probles. Doi the set of ll possible iput or x vlues of the fuctio/grph. Rge the set of ll possible output or y vlues of the fuctio/grph.. y x ***This is the pret fuctio for squre root.*** Doi Rge. y x. y x Doi Rge Doi Rge

14 . y x. y x Doi Rge Doi Rge Uder the rdicl sig: Outside of the rdicl sig: 6. Describe how to obti the grph of y x fro the pret fuctio 7. Fid the doi d the rge of the fuctio without grphig y x 9 Doi Rge Hoework: pge, 6-9,, 6, 9-, -9odd,

15 Algebr II 7. Grphig Cube Root Fuctios Dy Tody I grphig cube root fuctios. I successful tody whe I c grph cube root fuctios. It is iportt for e to kow/do this becuse cube root grphs re used to help solve rel-world probles. Doi the set of ll possible iput or x vlues of the fuctio/grph. Rge the set of ll possible output or y vlues of the fuctio/grph.. y x ***This is the pret fuctio for cube root.*** Doi Rge EVEN ODD NEITHER. y x. y x Doi Rge Doi Rge EVEN ODD NEITHER EVEN ODD NEITHER

16 . y x Doi Rge EVEN ODD NEITHER. Fid the equtio for the grph below. Hoework: pge -, 7, 8, -9odd,, 9

17 Algebr II 7.6 Solvig Rdicl Equtios Tody I solvig equtios tht coti rdicls or rtiol expoets. I successful tody whe I c solve equtios cotiig rdicls or rtiol expoets. It is iportt for e to kow/do this becuse these equtios c be used to solve rel-world probles. Whe solvig equtio with oe rdicl, first isolte the rdicl the eliite it. ***Alwys check your swers.***. x 0. x. x 8 6 Whe solvig equtio with two rdicls, first rewrite the equtio so tht you hve oe rdicl of the se power o ech side of the equl sig. The eliite the rdicls. ***Alwys check your swers.***. 6x x 0. x 6 x 6. x 8 x 0 7. x x 8 x 8 8. INTERSECT EXTRANEOUS SOLUTIONS

18 9. The strigs of guitrs d pios re uder tesio. The speed v of wve of o the strig depeds o the force (tesio) F o the strig d the ss M per uit legth L ccordig to the forul v F L M. A wve trvels through strig with ss of 0. kilogrs t speed of 9 eters per secod. It is stretched by force of 9.6 Newtos. Fid the legth of the strig. 9. Why does x 8 hve o solutio? Hoework: pge #7-6 first colu oly, 69,7-7

Summer MA Lesson 4 Section P.3. such that =, denoted by =, is the principal square root

Summer MA Lesson 4 Section P.3. such that =, denoted by =, is the principal square root Suer MA 00 Lesso Sectio P. I Squre Roots If b, the b is squre root of. If is oegtive rel uber, the oegtive uber b b b such tht, deoted by, is the pricipl squre root of. rdicl sig rdicl expressio rdicd