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1140 Review Final - MAC 1140 Final Exam Review 1 The...

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MAC 1140 Final Exam Review 1. The distance formula between two points in the plane is d = p ( x 1 x 2 ) 2 + ( y 1 y 2 ) 2 . (a) Find the distance between the points (2,3) and (0,8). (ans. p 29) 2. The point-slope formula of a line is y y 0 = m ( x x 0 ). where m is the slope and ( x 0 ; y 0 ) is a given point on the line. (a) If two lines are parallel, how are their slopes related? What if perpendicular? (ans.parallel: m 1 = m 2 ; perpendicular: m 1 = 1 m 2 ) (b) Find the equation of the line that is parallel to the line 2 x + 4 y = 6 and goes through the point (1 ; 2). (ans. y = 1 2 x + 5 2 ;) (c) Do the same if the lines are perpendicular. (ans. y = 2 x ) 3. If f is 1 to 1, then it has an inverse function f 1 . (a) How are the range/domanin of f and f 1 related? (ans. D f = R f 1 ; R f = D f 1 ;) (b) If f is 1 to 1, and f (2) = 9, then f 1 (9) =? (ans.2) (c) Find the inverse function of f ( x ) = 3 x + 1 2 x 5 . (ans. f 1 = 1 + 5 x 2 x 3 ) (d) If (1 ; 4) is on f , (3 ; 4) is on g , and f is 1 to 1 and g is odd, then f 1 ( g ( 3)) =? (ans.1) 4. The formula for the vertex of a parabola is ( x; f ( x )) where x = b 2 a . (a) How is the vertex of a parabola and its max/min related? (ans. If a n < 0 ; then vertex is max point; If a n > 0, then vertex is min point.) (b) How to nd the range of a function? (c) Sketch f ( x ) = 2 x 2 + 8 x + 1. Find the max (or min) value of the function and nd the range of the function. (ans. max value = 9 ; range = ( 1 ; 9]) 5. Transformation of a graph.
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