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Stitz-Zeager_College_Algebra_e-book

# However that does not prevent us from proving that an

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Unformatted text preview: as a function of x. Find the domain and range of those relations which are functions. (a) {(−3, 9), (−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4), (3, 9)} (b) {(−3, 0), (1, 6), (2, −3), (4, 2), (−5, 6), (4, −9), (6, 2)} (c) {(−3, 0), (−7, 6), (5, 5), (6, 4), (4, 9), (3, 0)} (d) {(1, 2), (4, 4), (9, 6), (16, 8), (25, 10), (36, 12), . . .} (e) {(x, y ) : x is an odd integer, and y is an even integer} (f) {(x, 1) : x is an irrational number} (g) {(1, 0), (2, 1), (4, 2), (8, 3), (16, 4), (32, 5), . . . } (h) {. . . , (−3, 9), (−2, 4), (−1, 1), (0, 0), (1, 1), (2, 4), (3, 9), . . . } (i) {(−2, y ) : −3 < y < 4} (k) { x, x2 : x is a real number} (j) {(x, 3) : −2 ≤ x < 4} (l) { x2 , x : x is a real number} 2. Determine which of the following relations represent y as a function of x. Find the domain and range of those relations which are functions. (a) (b) y y 4 2 3 1 2 −4 −3 −2 −1 1 2 3 −1 1 −2 −4 −3 −2 −1 1 x −1 −3 (c) (d) y y 5 3 4 2 3 1 2 −3 −2 −1 1 −1 1 −2 −2 −1 1 2 x −3 2 3 x 4 5 x 1.4 Introduction to Functions 41 (e) (f) y y 3 4 2 3 1 2 1 2 3 4 5 6 7 8 9 1 x −4 −3 −2 −1 2 3 4 x 1 1 2 3 x (h) (g) y y 4 4 3 3 2 2 1 1 −4 −3 −2 −1 −1 x 1 −5 −4 −3 −2 −1 −1 −2 (j) (i) y y 9 8 7 6 5 4 3 2 1 −3 2 −1 − −1 5 4 3 2 1 123 −5 −4 −3 −2 −1 −1 x 1 2 3 5 6 x −2 −2 −3 −4 −5 −3 −4 −5 (k) (l) y y 5 5 4 4 3 3 2 2 1 1 −5 −4 −3 −2 −1 −1 1 2 3...
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