Answer Key
775
ANSWER KEY Chapter 1 Checkpoint 1.1 . f (1) =3 and f ( a + h ) = a 2 +2 ah + h 2 −3 a −3 h +5 1.2 . Domain = { x | x ≤2}, range = ⎧ ⎩ ⎨ y | y ≥5 ⎫ ⎭ ⎬
1.3 . x =0, 2, 3 1.4 . ⎛ ⎝ f g ⎞ ⎠ ( x ) = x
⎧ ⎩ ⎨ x | x ≠ 5 2
⎫ ⎭ ⎬ .
2 +3 2 x −5
. The domain is
1.5 . ⎛ ⎞ ⎠ ( x ) =2−5 x . 1.6 . ( g ∘ f )( x ) =0.63 x 1.7 . f ( x ) is odd. 1.8 . Domain = (−∞, ∞), range = ⎧ ⎩ ⎝ f ∘ g
⎨ y | y ≥−4 ⎫ ⎭ ⎬ . 1.9 . m =1/2. The point-slope form is y −4= 1 2
( x −1). The slope-intercept form is y = 1 2
x + 7
2 .
1.10 . The zeros are x =1± 3/3. The parabola opens upward. 1.11 . The domain is the set of real numbers x such that x ≠1/2. The range is the set ⎧ ⎩ 1.12 . The domain of f is (−∞, ∞). The domain of g is { x | x ≥1/5}. 1.13 . Algebraic 1.14 .
⎨ y | y ≠5/2 ⎫ ⎭ ⎬ .
⎧ ⎩ ⎨ 49, 0< x ≤1
1.15 . C ( x ) = 70, 1< x ≤2 91, 2< x ≤3 1.16 . Shift the graph y = x 2 to the left 1 unit, reflect about the x -axis, then shift down 4 units. 1.17 . 7 π /6; 330° 1.18 . cos(3 π /4) = − 2/2; sin(− π /6) =−1/2 1.19 . 10 ft 1.20 . θ = 3 π 2 +2 nπ , π 6 +2 nπ , 5 π 6 +2 nπ for n =0, ±1, ±2,…
1.22 . To graph f ( x ) =3sin(4 x )−5, the graph of y = sin( x ) needs to be compressed horizontally by a factor of 4, then stretched vertically by a factor of 3, then shifted down 5 units. The function f will have a period of π /2 and an amplitude of 3. 1.23 . No.
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