1. (18 pts) Consider the function f (x) = * +2 X (a) Find the domain of f. (b) Analyze f , f' and f".\fStrategy For Sketching y = f(x) : 1. Identify the domain for y = /(x). the largest set of x-values on which f is defined. 2. Analyze J. a ) zeros ( x1 0), ( X2, 0 ), .. . set f ( x ) = 0 and solve for x. 6 ) yintercept (0, y,) set x= 0 and plug it into f to find y, c ) asymptotes i ) vertical asymptotes, ( eans ) x = 0 ., x = az lim f (x)= =00 OR lim f (x)= +0 Review Section 2.2 ii ) horizontal asymptotes (eqns ) y=b,, y=boz ( im fix ) = b, OR lim f(x ) = b, X700 X - of Review section 2.5 d ) " hole " ex. lim ( x+1 ) ( or)_ lim ( *+1 ) = 1+1 = 2 X71 X 71 There is a graphical feature in this graph that appears as a hole at ( 1, 2) o e ) symmetry this is discussed f ) periodicity later3. Analyze S'. a] find the critical numbers off coordinates f ' ( c ) = 0 or f ( c) does not exist and c is indomain b) find intervals of increasing (f'20) and decreasing (fico). * make a number line! intervals consider the sign of fo mark critical #S, points not in our doman. c) identity local extrema Represent as coordinates use First Derivative Test. d) identify absolute extrema. Represent as coordinates use EVT, if possible or use information from ( b ) and ( c ) 4. Analyze J". a ) identify places for potential points of inflection (PPOI ). Find where f" ( x) =0 and f" ( x) does not exist b ) find intervals of concave up (f"20] and concave down (f"