# For polynomials x if none of the signs change the

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For polynomials x if NONE of the signs change, the function is ________________________. x if ALL of the signs change, the function is __________________________. x if SOME signs change and some stay the same, the function is __________________________. For quotients of functions x even even ________________________________________. x odd odd _________________________________________. x even odd or odd even ________________________________. A function that has y-axis symmetry is called and even function. For such functions, ( ) ( ) f x f x ± for all x in the domain of f. A function that has origin symmetry (180 °rotational symmetry) is called an odd function. For such functions ( ) ( ) f x f x ± ± , for all x in the domain of f ff C x ts gtx txt 41 1 3 next 2.6 13 3 2 3 3 2 s x 4 3 huh 2 3 3 gW 1 2 4 3 2 3 3 since E the function even x 4 3 Neither Neither gl xl tgcxlgc.in gcxivftl IC tl3 C t Et3ttrfml C m73 vLtl Its E 2 5 1 2 It3tt rink GIT 5.3dm ODD ODD EVEN ODD Neither even EVEN ODD

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It helps to have these rules of thumb memorized, but it’s never an excuse for not knowing how to perform the algebraic test. In fact, you will be asked to do just that on your exam! Putting it all together so far: Example 7 For each of the following, find the domain, end behavior, x-intercepts, y-intercepts, any symmetry, and find and label all discontinuities. Use your collected information to sketch a graph. (a) 2 2 2 2 4 ( ) 3 9 30 x x f x x x ± ± ² ± (b) 2 4 8 ( ) 2 x x g x x ² ² 4 1 2 hole x 2 2 y int let x D De C a 2 ul z Df x 1 1 2 r cxt 2 gg jIffY o Fo E EBM 4 41 1 Iim f 1 1 2 3 HA 9 43 1 m ga Xed EBM Xt lim f x _43 2 2 Iim gCx xx x Zz x Sy gtx 4fx 2t Review xtz 4 2 8 1 Get into groups of 2 3 xt2 Tow w the gC f y g Neither review

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