61. A linear function 5. True ( ) = + will be f x mx b odd provided 6. True (− ) ( = − f x f x ) . (− ) (mx That is, provided + = − + m x b 7. Linear relation, > 0 m ) . b −mx + = −mx 8. Nonlinear relation b − = −b b b provided (− ) ( 13. a. 20 = f x f x ) . (− ) That is, provided + = + m x b mx . b −mx + = + b mx b −mxb = mx 0 10 0 0 = 2mx = 0 m So a linear function ( ) = + will be b. Answers will vary. We select (3, 4) and f x mx b provided = 0 . m (9, 16). The slope of the line containing even Section 2.2 62. The French word means climb”. monter “to Urban legend has it that the usage of for slope m 1. No, the relation is not a function resulted from However, this is monter. because the coordinate 1 is paired x- uncertain. Another theory is that the comes m with two different coordinates, 5 y- from the term of the slope”. “modulus and 12. 63. The grade of a road is related to the slope of a Yes, the relation defined by = 2x + 1 2. y line in that both terms describe A “steepness”. is a function because it is a non- 4% grade means that for every 100 units of line, which means each horizontal change in the road there is 4 units of will be paired with a vertical change. Answers will vary. distinct y-coordinate. 64. The pitch of a roof/staircase is related to the 3. scatter diagram slope of a line in that both terms describe Answers will vary. “steepness”. 4. = y kx
61. A linear function f ( x ) = mx + b will be odd 5. True provided f (− x ) = − f ( x ) . 6. True That is, provided m (− x ) + b = − (mx + b ) . −mx + b = −mx − b b = −b 7. Linear relation, m > 0 8. Nonlinear relation provided f (− x ) = f ( x ) . 13. a. 20 That is, provided m (− x ) + b = mx + b . −mx + b = mx + b −mxb = mx 0 = 2mx m = 0 0 10 0 So a linear function provided m = 0 . f ( x ) = mx + b will be even b. Answers will vary. We select (3, 4) and (9, 16). The slope of the line containing 62. The French word monter means “to climb”. Urban legend has it that the usage of m for slope resulted from monter. However, this is uncertain. Another theory is that the m comes from the term “modulus of the slope”. 63. The grade of a road is related to the slope of a line in that both terms describe “steepness”. A 4% grade means that for every 100 units of horizontal change in the road there is 4 units of vertical change. Answers will vary. 64. The pitch of a roof/staircase is related to the slope of a line in that both terms describe “steepness”. Answers will vary. Section 2.2 1. No, the relation is not a function because the x- coordinate 1 is paired with two different y- coordinates, 5 and 12. 2. Yes, the relation defined by y = 2x + 1 is a function because it is a line, which means each will be paired with a distinct y-coordinate. 3. scatter diagram 4. y = kx non-
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