AN28 Answers: Chapter 4 35. Step 1: ( ) ( )( ) ( )( ) = + − − − R x x x x x 3 1 2 3 2 2 3 ; domain: { } ≠ ≠ x x x 3 2 , 2 Step 2: In lowest terms, ( ) = + − R x x x 3 1 2 Step 3: y-intercept: − 1 2 ; x-intercept: − 1 3 Step 4: Vertical asymptote: = x 2; hole at ( ) − 3 2 , 11 Step 5: Horizontal asymptote: = y 3, not intersected Step 6: 10 23 25 10 Step 7: y 8 x 10 (6, 4.75) x 5 2 y 5 3 21, 2 3 , 0 2 1 3 1 2 0, 2 , 211 3 2 37. Step 1: ( ) ( )( ) = + + + R x x x x 3 2 3 ; domain: { } ≠ − x x 3 Step 2: In lowest terms, ( ) = + R x x 2 Step 3: y-intercept: 2; x-intercept: −2 Step 4: Vertical asymptote: none; hole at ( ) − − 3, 1 Step 5: No horizontal or oblique asymptote Step 6: 4 28 24 4 Step 7: y 5 x 5 (22, 0) (23, 21) (24, 22) (0, 2) 2 2 1 2 , 5 2 39. 1. ( ) ( ) ( )( ) = − − − + H x x x x 3 2 2 2 ; domain: { } ≠ − ≠ x x x 2, 2 2. In lowest terms, ( ) = − + H x x 3 2 3. y-intercept: − 3 2 ; no x-intercept 4. Vertical asymptote: = − x 2; hole at ( ) − 2, 3 4 5. Horizontal asymptote: = y 0; not intersected 6. 10 28 210 4 7. y 10 x −7 (−3, 3) y = 0 x = −2 Q3 , − R 3 5 Q0 , − R 3 2 Q2 , − R 3 4 41. 1. ( ) ( )( ) ( ) = − − − F x x x x 1 4 1 ; 2 domain: { } ≠ x x 1 2. In lowest terms, ( ) = − − F x x x 4 1 3. y-intercept: 4; x-intercept: 4 4. Vertical asymptote: = x 1 5. Horizontal asymptote: = y 1; not intersected 6. 6 26 26 6 7. y 5 −5 x −5 5 (0, 4) (2, −2) y = 1 x = 1 Q5 , R 1 4 (4, 0) 43. 1. ( ) ( ) = + G x x x 2 ; 2 domain: { } ≠ − x x 2 2. G is in lowest terms 3. y-intercept: 0; x-intercept: 0 4. Vertical asymptote: = − x 2 5. Horizontal asymptote: = y 0; intersected at ( ) 0, 0 6. 1 26 24 6 7. y 3 −7 x 3 −7 (−1, −1) (0, 0) (−3, −3) x = −2 y = 0 Q1 , R 1 9
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