Properties of Graphs of Polynomial Functions Terminology Associated with Graphs of Polynomial Functions

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1 Properties of Graphs of Polynomial Functions Terminology Associated with Graphs of Polynomial Functions Detennine what types of polynomial functions/, g, and hare graphed below Give a reason for your conclusions based on the zeros of each function + j _, r g(x) ;;, As we begin to study the graphs of polynomial functions, there are other properties of graphs that now can be identified For the remainder of this lesson, we will define terms and then we will identify these tenns on from the graphs of the given functions

2 CL po\ lv'\u',\ +o U\\lf"t Label and identify the relative maximum(s) on the graphs of the functions pictured to the right : : : 1 : i l T l ; ; ) (-2,d- 1 i \ (2, o) G\ toc<6- -b \ Label and identify the relative minimurn(s) on the graphs of the functions pictured to the right : : L : i :, : : -i\v ro,jt (-2,-'1) t2,-y) Define absolute minimum fohj-( ) Q -+ 1t1Asl Lo a-- "' Label and identify the absolute minimum(s) on the graphs of the functions pictured to the right,-5,1- i, '' ' ' No 01 lv\-e Ti> f-5' +1:r,: ; = l i / ' + \ : :1 1 ; T j r 1 1 J \ i(, )

3 Define absolute maximum Label and identify the absolute maximum(s) on the graphs of the functions pictured to the right Define point of inflection () fc' a, How many points of inflection does the graphed function below have? Label their approximate locations on the gra h Label and identify the coordinates of all points of inflection for the graphed functions below : ' =

4 Define intervals of concavity &f llf\ -0 +',x,- f r i ; I J=i}ii '-"f ( ) ca) e : i i l : i (-co, -:i) u (-, oo) Identify the interval(s) on which C&AJ,,( r'mi"" 1\1\ (-a>, " ft - the graphed functions to the right " r- are concave up & concave down _ 2 - -;, (-1, 5) Domain: (- (%) ) CO Range: (_-cc ; co) j(x) > 0: ( ) () ( 'S, GO) S Left End Behavior: Zeros and their multiplicities: X:: -'2 1 I 3 CM, ljcif>ltc-4 d t End Behavior: j(x) < 0: (-oo \ J -lj U ( \, / j(x) is increasing: (-oo ) -0u c ) oo) Relative Mini um(s): Point(s) of Inflection: I A >Ai'-fi,l (-, ' ) ol, (-1""2 5- \_ (j 1 7) - J- :4, ;i) Int ls of x - values where j(x) is cfecreasing: (-\, 2) Absolute Maximum(s): j(x) is concaves:,: Relative Maximum(s): po,j- (-\, c;) Absolute Mjnimum(s): N f(x) is concave down:

5 (1, 6) Domain: (- C:::C, 00 j(x) > 0: Zeros and their multiplicities: x -s x:2 0, pu 1, i X ': -2 ho ca >NJ f uc;_ j(x) < 0: (-rd J -s) u (a, oo) Left End Behavior: Right End Behavior: j(x) is increasing: (-oo ) -4) U (-2, i) Relative Minimum(s): f>o", (-, t>) Point( s) of Inflection: I J- '<:i (,3) J l, o (- ;2, i-:_o)=- (-, i A, '* ) ()&) - ce j(x) is decreasing: (-4 ) -:2)v(,, co) Absolute Maximum(s): ftj' (J,c) 1J-<t(-:1 1 0) (I, '-) (-2-:_I ) C )-: -i 1 3)\ f-in-te _ rv _ a_ls _ o _ f _ x elative Maximum(s): po, (---+, ) GHd (_\ ) c) Absolute Minimum(s): -- j(x) is concave up: (-3, -t) &v\t-, v _ a lu_e s - w - hēr- e j( -x ) _ i_s - co _ n cāv e _ d o _ w _ n_:, (_- t:)o) - $) L) ( - i, )

6 Name LC-'---=--'= k Date Period Day #18 Homework For the function,/{x), pictured below, identify the following characteristics in exercises 1-18 (0, 5) l Domain: 4 j{x) < 0: C-00 J -;)ol1, «>) 2 Range: 5 Left End Behavior: A'> -oo) "t'ul), _ o0 3 f{x) > 0: (- 3, 1) 6 Right End Behavior: 7 Zeros and their multiplicity: 8 Type of Function 9 Possible Equation: 'X, = - w, mvlfl: Gv \-i< blc "' 11 :"\ ( _ i,1 M W\vl hd "'-,ti ):: -0\"x-tJ 'X, - ; ')-: ( 1N1'T"\ o r 1 'it i-' "<:\ ' l'\'\,a pli ', &{, i 10 f{x) is increasing: (-oo, ii) 13 Relative Minimum(s): 11 f{x) is decreasing: 14 Absolute Maximum(s): fo, to, s) 12 Relative Maximum(s): \W- ()"' (c, 5) 15 Absolute Minimum(s): 17 f{x) is concave up: 18 f{x) is concave down: (-a>) -3) U (-, 5, c:o)

7 (-2, 2) Left End Behavior: Right End Behavior: 3-1 I\ 19 Domain: (_ -c::o 1 ())) Range: (_-(XJ) 00) Zeros and thei multiplicities: t M"l' ')C -'1 )( : _,,y - I\ - L :) fts?< -oo) +l>c) -oo /Jrc, 'X IJio'o0 1 t ) co 23 j(x) is 24 Intervals of x - values increasing: where j(x) is decreasing: 3 \ \ 20 j(x) > 0: (-4, -,) lj ( i, ex>) f(x) < 0: 22 Type of Function and why: Qv,J-ic c, 1kt u l f C,:-\irca t,c s 25 Relative Maximum(s): 26 Relative Minimum(s): 27 Absolute Maximum(s): --re f l "' ::k 0-3),-J &'\'\L 28 Absolute Minimum(s): 30 Approximate intervals of x- values wheref(x) is concave up: 31 Approximate intervals of x - values where f(x) is concave down:

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