Exercises-Functions- - x 3-x b f R โ†’ R f x = x ย | x | c f R โ†’ R f x = x x 2 1 d f Z โ†’ Z f x = x ย-1 x e f R โ†’ R f x = x x โˆˆ Q-x x โˆˆ R

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MA100, Fall 2010, PART 1: Precalculus Functions - Exercises-1 1) Which of the sketches a) to f) represent functions? For each sketch representing a function, state the function’s domain and range. 2) Find the domain of the functions: a) f ( x ) = 2 x 2 - 5 x 2 x + 5 b) f ( x ) = x 2 - 3 x + 2 x 2 - 4 c) f ( x ) = 1 + 2 x - 4 + 3 x + 2 x 2 - 5 x + 6 d) f ( x ) = x - 2 e) f ( x ) = x - 2 + 3 x + 2 x 2 - 5 x + 6 f) f ( x ) = r 2 - x 2 x - 3 g) f ( x ) = r 8 - 4 x 4 x + 2 + 1 x h) f ( x ) = 5 x 2 + 6 x + r 1 3 - x i) f ( x ) = 5 5 x 2 + 6 x j) f ( x ) = 3 r 1 3 - x + 3 x + 2 1
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3) Consider f : R R , f ( x ) = 3 x - 4 , x ( -∞ , 0] 2 , x (0 , 2) 3 - 2 x - 2 x 2 , x [2 , ) Find f (2) ,f ± 1 5 ² ,f ± - 1 5 ² ,f ± 7 4 ² . 4) Determine the range of the following functions: a) f : R R , f ( x ) = 2 x + 1 b) f : [ - 1 , 5] R , f ( x ) = 2 x + 1 c) f : ( -∞ , 0] R , f ( x ) = 2 x + 1 d) f : {- 1 , 0 , 1 , 2 , 3 } → R , f ( x ) = 2 x + 1 e) f : [ - 1 , 1] ∪ { 2 , 4 } → R , f ( x ) = 2 x + 1 5) Decide which functions are odd, which are even and which are none: a) f : R R , f ( x ) =
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Unformatted text preview: x 3-x b) f : R โ†’ R , f ( x ) = x ยท | x | c) f : R โ†’ R , f ( x ) = x x 2 + 1 d) f : Z โ†’ Z , f ( x ) = x ยท (-1) x e) f : R โ†’ R , f ( x ) = ( x, x โˆˆ Q-x, x โˆˆ R \ Q Answers to selected exercises: 1) b) It is a function; the domain is { a,b,c } and the range is { 2 } d) It is a function; the domain is { a,c } and the range is { 2 } f) It is not a function. 2) b) x โˆˆ (-โˆž , โˆž ) \ ยฑ 2 d) x โˆˆ [2 , โˆž ) g) x โˆˆ ยฑ-1 2 , 2 ยณ \ 0 i) x โˆˆ (-โˆž , โˆž ) 4) b) [-1 , 11] d) {-1 , 1 , 3 , 5 , 7 } e) [-1 , 3] โˆช { 5 , 7 } 5) b) odd d) odd 2...
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This note was uploaded on 10/14/2011 for the course MATH 100 taught by Professor A during the Fall '10 term at Wilfred Laurier University .

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Exercises-Functions- - x 3-x b f R โ†’ R f x = x ย | x | c f R โ†’ R f x = x x 2 1 d f Z โ†’ Z f x = x ย-1 x e f R โ†’ R f x = x x โˆˆ Q-x x โˆˆ R

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