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Math 005A-Summer 2021 Page 2of 5 July 20, 2021 3. Consider the function f(x) = = 1 -4 12 - 9 and answer the following. (a) [2 points] State the domain of the function. f(x) =x2 - 4 * 2-9 *"-9 +0 (denominator can't be sen) X2#9 cdomain * R - 8- 3, 85 * * +3 (b) [3 points] Find the r & y-intercepts, if any. Denote them as ordered pairs. for *- intercut 4 -Intercept : 7 = x2-4 *- int . 7 (0 , 4 ) 7=0 - X1-4 * 2 -4 -0 * 2-9 * =0-4 x- int . = ( 2,0) &(-2,0) (c) [4 points] State the intervals where f is increasing/decreasing. f'(r) = -10r fux) = - 10x (12 - 9)2 ( x 2 - 9 ) 2 increasing f'( x ) >0 decreasing f' ( x ) O -10x 20 - XCo * + -3 x E (0, 3) U ( 3,00) X E (-DO, - 3) U (- 3,0) (d) [4 points] State the intervals where f is concave up/down.f"(x) = 30(x2 + 3) (x2 -9)3 f" ( * ) = 30 (* 2 + 3 ) ( x 2 - 9) 2 Concave up concave down to f " ( *) 20 f " ( x ) 20 30 ( x2 + 3 ) 30 (x2+3) ( x -3)5 ( x43 )3 30 ( x 2 + 3 ) ( x -3)3 ( x 13 ) 3 20 x E (-3, 3 ) X E (-00, -3) 0(3,09) Math 005A-Summer 2021 Page 3of 5 July 20, 2021 (e) [4 points) State the horizontal and vertical asymptotes if any (You must assert them using limits!). (f) [4 points] Sketch f(r). Clearly label any horizontal asymptotes, vertical asymp- totes, intercepts and extrema used to graph f (I)