Download Degree:_ L.C.:- and more Summaries Algebra in PDF only on Docsity!
Worksh eet 5.2 & 5.
Homework for^ Algebra^2
Polynomial functions^ have^ positive,^ integer^ exponents^ applied^ to variables.^ They do not^ include
absolute values, roots, or negative exponents^ that^ are^ applied^ to^ variables,^ and^ they^ do^ not^ include variables in^ the denominator. Classify the fotlowing functions.^ Decide^ if^ the^ function^ is^ a^ polynomial^ function.^ If^ it^ is^ a
the relative maximum(s)^ and^ the^ relative^ mtnr
lvnomial function. state^ its^ de^ t^ leadine^ coefficient^ and l. (^) lU):2x -27'Ya +^9
Polynomial?_ Degree:_ L.C.:_ Tvpe:
2./(x):x*TE
Polynomial?_ Degree:_ L.C.:_ Tvpe:
- (^) .f(x):3x'2 +^ 4x-t^ t
Polynomial? (^) _ Degree:_ L.C.:- Type:
Polynomial? (^) _ Degree:_ L.C.:_ Tvpe:
4. f(x)=*'Ji+x-5 5. .f(x)=lx-51+
Polynomial?_ Degree:_ L.C.: Type:
/(x): (x^ - 5)2^ +^3
Polynomial?_ Degree:- L.C.: Type:
- (^) /(x):-x'+36x/ -3x+
Polynomial?_ Degree:_ L.C.:_ Type:
- (^) {x):25 -
Polynomial?_ Degree:_ L.C.:- Type:
s- (^) f (*)=zJi^ -s
Polynomial?_
Degree:_ L.C.:-
Tvoe:
Given the graph,^ describe^ the^ end^ behavior^ of^ the^ function. Also,^ state^ the real^ zeros,^ the^ y-intercept,
As x-> +oo.flx)^ -+_
As x-> -*,-flx)^ -+_
Real Zeros: y-intercept:_ Relative maximum(s):
Relative Minimum(s):
As x-+ +.o.lx)^ -)_
As x-+ -*"J(x) -+_
Real Zeros: y-intercept:_ Relative maximum(s): Relative Minimum(s):
As x-+ +oo,l(x)^ -+_ As x-+ -*.JU) -)_ Real Zeros: y-intercept:_ Relative maximum(s): Relative Minimum(s):
lvcn rl UI
13.JU): -nr +^1
As x-+ +co.flx)^ -+_
As x-> -cr, (^) flx) -+
14./(x): f +^ 2x
As x-+ +oo.flx)^ -+_ As x-+ -a, (^) flx) -+
As x-+ +co"lx)^ +_
As x-+ -oo.^ l[x) -+
15..flx):3x6 (^) -4xr
As x-+ +a.flx) =)_
As x_+ _co,^ fl'x) -+
- (^) JU): -xb +^ 2;3 (^) - x
Given the function. describe the end behavr
funct
the function.
- (^) flx): 5(x (^) - 1)(x (^) - 2)(x (^) -3)
- (^) .flx): x4 (^) -2x -3 23.^ JU):2(x +^ 2121x^ +^412
Given the graph.^ what^ is^ the lowest^ degree^ that the^ tunctton^ could^ have t7.
Number of turning points: Lowest Degree:_ Real Zeros: y-intercept:_ Relative maximum(s):
Relative Minimum(s):_
As x-+ +*.J@)^ -+_
As x-+ -cr, (^) flx) -+
Number of turning points: Lowest Degree:_ Real Zeros: y-intercept:_ Relative maximum(s):_ Relative Minimum(s):_ As x-+ +oo,flx)^ -)_ As (^) x-+ -cr, (^) flx) -+
t9.
Number of turning points: Lowest Degree:_ Real Zeros: y-intercept:_ Relative maximum(s):_ Relative Minimum(s):_ As x-+ +oo,flx)^ -+_
As x-+ -oo.^ l[x) -+
describe the end behavior. 13./(x): -x'+ 1 t\ As x-+ +*,/(x) -+:g As x-+ -cr, (^) f(x) (^) -> @
14./(x): (^) x5 + (^) 2x
Asx-+ +*,flx)^ -+_
As x-> -"o. /{'x) ->
15.f(x):3x6 (^) - 4 ,!/ As x-> +a,^ flx) -+ As x-> -cr, (^) flx) -+
As x-+ +co,^ flx) -+ As x-> -cn, (^) f(x) -+
I
^ t-orlaj Given the what is the lowest that the function could have? l) oq rt^ a
Graoh the functi
-rO,1.
-1?
{
Number of turning pgints: (^) { Lowest Degree: (^3) =
Real Zeros : (^1) -1.5r-t, l (^) rt, 5J
y-intercept, (Ol-a)^ 1-a.3)
Relative maximum(s)' ii'S )
Relative Minimum(r)@
As x-> +*,/(x)^ -+oo Asr-+ -cr.,f(x) --y (^) -
Number of turning points: Lowest Degree:_ Real Zeros: y-intercept:_ Relative maximum(s): Relative Minimum(s):
As x-> +x,flx)^ +_
As x-> -cr,l@) (^) -+
Number of tuming points: Lowest Degree: {
Real Zeros: l-5.- l. I
y-intercept: (Or^ t) Relative maximum(s): (or^ t ) Relative Minimum(s): (^) Gj,.3)
As x-+ +*,J(x)^ a ao
As x-> -oo, (^) fl'x) (^) -> @ on.
20. fl*): 5(x - lXx - 2)(x -3) 21. JU): ir-3x ff
tt)-y3-ax- ]
- (^) lU):x4-2x- uo- ir^ tl f o-u^ ieLJ n Q"r^ o)og.^. DocS ao 8oc-*at-. .,^ o,^ e c.q 1c.., I^ o^ *a^ C
ffi
vET' (or-3)
- (^) flx): 2(x +^ 2121x +^412
)= Efuffi :A (^) +-rCx?
