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# HW5 - MAP 103 Prociency Algebra Homework#5 DUE THURSDAY...

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MAP 103: Proficiency Algebra Homework #5 DUE: THURSDAY, OCTOBER 8, 2009 1. Let X = { 0 , 1 , 2 , 3 , 4 } and Y = { 0 , 2 , 4 , 6 , 8 } . Suppose f : X -→ Y is relation between the two sets so that the set X is the domain of the relation and Y is the range. Could f be a function? 2. Find the equation of a linear function in the form f ( x ) = ax + b satisfying that f (1) = 3 and f (4) = 7 . Using your function, find f ( - 1) . What is the domain of f ? 3. On the interval - 5 6 x 6 5 , graph the relation y = | x | . (a) From definitions, is y = | x | a function? (b) Is y = | x | one-to-one? (c) Is y = | x | onto? 4. Let Γ f denote the graph of a function f. Determine if following sets give functions. (a) Γ f = { ( x, y ) R × R | y = x + 1 } (b) Γ f = { ( x, y ) R × R | y = x 2 + x } (c) Γ f = { ( x, y ) R × R | y = | x | x } (d) Γ f = { ( x, y ) R × R | y 2 = x 2 } 5. For each of the functions below, find its respective domain. (a) f ( x ) = x 2 + 2 x + 1 (b) f ( x ) = 1 + 1 - x (c) f ( x ) = x 2 - 1 (d) f ( x ) = 5 x 4 x +1 6. Let f ( x ) = ( x + 1 x > 2 - x + 1 x 6 2 . Find f (0) and f (2) . 7. Sketch the graph of a function y = f ( x ) that satisfies the following properties:
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