chapter 1 9 - SECTION 1.1 FOUR WAYS TO REPRESENT A FUNCTION...

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Unformatted text preview: SECTION 1.1 FOUR WAYS TO REPRESENT A FUNCTION El 9 (c) As in part (b), there is $1000 tax assessed on $20,000 of T(in dollars) income, so the graph of T is a line segment from (10,000, 0) to (20,000, 1000). The tax on $30,000 is $2500, so the graph of T for a: > 20,000 is the ray with initial point 1000 (20,000, 1000) that passes through (30,000, 2500). 2500 10,000 20,000 30,000 I (in dOHHIS) 56. One example is the amount paid for cable or telephone system repair in the home, usually measured to the nearest quarter hour. Another example is the amount paid by a student in tuition fees, if the fees vary according to the number of credits for which the student has registered. 57. f is an odd function because its graph is symmetric about the origin. 9 is an even function because its graph is symmetric with respect to the y-axis. 58. f is not an even function since it is not symmetric with respect to the y—axis. f is not an odd function since it is not symmetric about the origin. Hence, f is neither even nor odd. 9 is an even function because its graph is symmetric with respect to the y-axis. 59. (a) Because an even function is symmetric with respect to the y—axis, and the point (5, 3) is on the graph of this even function, the point (—5, 3) must also be on its graph. (b) Because an odd function is symmetric with respect to the origin, and the point (5,3) is on the graph of this odd function, the point (—5, —3) must also be on its graph. 50. (a) If f is even, we get the rest of the graph by (b) If f is odd, we get the rest of the graph by reflecting about the y—axis. rotating 180° about the origin. y y 0 0 x x 61. f(:1:) : 13—2. 62. f(:c) = 23—3. _ 1 1 1 1 f(—.’ZI):(—.’E) 2: :_ —.’L' 2 “IL‘ _3: :_ (_$)2 $2 f( ) ( ) (—{II)3 _$3 : $_2 : f (E 1 _ . l.) =——3=—<w 3)=—f<m> So f is an even function. cc y . So f is odd. 63. f(;c) : 332 + c, so f(—a:) = (—a:)2 + (—a:) = $2 — m. Since this is neither f(av) nor —f(:c), the function f is neither even nor odd. ...
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