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Math 153 exam_2_soln

# Math 153 exam_2_soln - MATH 153 NAME SQLIIIIQHS EXAM 2...

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Unformatted text preview: MATH 153 NAME: SQLIIIIQHS EXAM 2 MARCH 4, 2008 Snow YOUR WORK FOR FULL CREDIT. 1. Find the slope-intercept form of the equation of the line passing through the points (1, —2) and (3, 4). Sketch the line. 4—(—2) 6 m = 3—1 =§=3 y—(—2) = 3(3—1) y+2 = 33—3 3; = 33—5 2. Find the zeros of the function ﬂue) = 3:3 — 8:5. Simplify your answers. 33—81: = 0 1112—8): 0 :1: = Oor 3:2:8 a: = 0 or x=:h2\/§ 3—2 1-2—53: 3—2-20 and Luz—5.17960 \$32 and x(:r—5)aé0 3:22 and \$760.5 3. Find the domain of the function f (3:) = . Give your answer using interval notation. Dorinain of f: [2.5) U (5.00) t 4. Write the circumference C of a. circle as 9. function of its area A and simplify. Recall: If r is the radius of a circle, then A = m2 and C = 2m. A=1rr r:— ‘1 ll [FER ”ID:- v .2: ll} 0 u I M N) .1 3} lb:- ""1 II to :1 II N) =14 ‘33 3: “£5“ 0 = 2V1rA 1 9. Let f(:c) = x9 _ .4 (3.) Find f 09, simplify, and ﬁnd‘ its domain. (f 0 9M") f'(9('1:)) ﬂm+m 1 (a; + 2)2 — 4 1 1 '32 + 4x 1 :z':(:c + 4) and 9(3) = 58+ 2. ll ll II Domain of f 'o g = (—00, —4) U. (41,0): U. (0, 00) (b) Find '9 o f, simplify, and ﬁnd its domain. (3%)) 1) ll ‘Q ”'5' "Ha (9 0 flf'w') I] ﬁn- r—‘\ H” I .p. II II Domain of g o f = (—003, —2) U (—2, 2) U (2', 00) 10. A rectangle. is bounded by the 'm—axis and the semicircle-y = x] 25 — 3:5 (see ﬁgure on the board). Write the area A of the rectangle as a. function of m, and determine the-domain ' of the function. A = length - Width = 2.1: - y 2mv25 - 32:, 0. < a: <- 5 6. Write an expression fer the function Me) with the shape. of f (at) = m2 but moved 4 units to the right and 7 units downward. Simplify your answer. M9?) = (55 — '4? — 7 Mat) 2 5:2 — 83 + 9 4—2:”, x<2 7. Sketch the graph" ofthe Met“ “2”) = { z + 1. I > 2 8. Given f (3:) = 52: — :32, ﬁnd the'diﬁ'erence quotient w and simplify. f(2 H!) - f E?) = [5(2 + h) - C3 + ’02} - [5(2) - (2)2] h h _ [10+5h — (4+4h+h2')] — [10 —4] _ .___.__h—— _ 10+5h‘-4-—'4h—h2— 10+4 _ _._._.___h___.___.___. _ h — h? " h h(1 - h) h l—h ll ...
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