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Unformatted text preview: 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 x 5, graph the relation y = x. (a) From deﬁnitions, is y = x a function? (b) Is y = x onetoone? (c) Is y = x onto? 4. Let Γf denote the graph of a function f. Determine if following sets give functions. (a) Γf = {(x, y ) ∈ R × R  y = x + 1} (b) Γf = {(x, y ) ∈ R × R  y = x2 + x} x (c) Γf = {(x, y ) ∈ R × R  y = x } (d) Γf = {(x, y ) ∈ R × R  y 2 = x2 } 5. For each of the functions below, ﬁnd its respective domain. (a) f (x) = x2 + 2x + 1 √ (b) f (x) = √+ 1 − x 1 (c) f (x) = x2 − 1 5x (d) f (x) = 4x+1 6. Let f (x) = x+1 −x + 1 x>2 . Find f (0) and f (2). x2 7. Sketch the graph of a function y = f (x) that satisﬁes the following properties: • y = f (x) has an xintercept at (−4, 0) and (3, 0). • y = f (x) has a y intercept at (0, 2). • y = f (x) is decreasing on the interval (−∞, −1), [0, 2] • y = f (x) is increasing on the interval [2, ∞). 8. Using an appropriate domain, make a table of values and graph the following functions. 1 (a) f (x) = x + 1 √ (b) f (x) = x + 2 (c) f (x) = x5 (d) f (x) = 2 9. Let f (x) = x + 1 and g (x) = 2x + 3. Find (f + g )(x), (f − g )(x), (f g )(x), and (f + g )(0). 10. Consider a system of linear inequalities: the system? y 2x + 1 . What is the domain of the solution to y > 4x + 3 ...
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This note was uploaded on 04/18/2010 for the course MAP 103 taught by Professor Staff during the Fall '08 term at SUNY Stony Brook.
 Fall '08
 Staff

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