Section 4.6 AN27 21. Step 1: ( ) ( )( )( ) = − + − R x x x x 3 1 2 2 ; domain: { } ≠ ≠ − ≠ x x x x 1, 2, 2 Step 2: R is in lowest terms Step 3: y-intercept: 3 4 ; no x-intercept Step 4: R is in lowest terms; vertical asymptotes: = − = = x x x 2, 1, 2 Step 5: Horizontal asymptote: = y 0, not intersected Step 6: 5 24 25 4 Step 7: y 5 x 5 x 5 2 x 5 22 x 5 1 y 5 0 0, 3 4 3 20 23, 2 3, 3 10 2 24 7 , 3 2 23. Step 1: ( ) ( ) ( )( ) ( )( ) = + − + + − H x x x x x x 1 1 4 2 2 2 ; domain: { } ≠ − ≠ x x x 2, 2 Step 2: H is in lowest terms Step 3: y-intercept: 1 16 ; x-intercepts: −1, 1 Step 4: H is in lowest terms; vertical asymptotes: = − = x x 2, 2 Step 5: Horizontal asymptote: = y 0, intersected at ( ) ( ) −1, 0 and 1, 0 Step 6: 1 24 21 4 Step 7: y x 5 0.3 (3, 0.12) (1, 0) (1.5, 20.11) (21.5, 20.11) (21, 0) (23, 0.12) 0, 1 16 x 5 22 x 5 2 y 5 0 25. Step 1: ( ) ( )( ) = + − + F x x x x 1 4 2 ; domain: { } ≠ − x x 2 Step 2: F is in lowest terms Step 3: y-intercept: −2; x-intercepts: −1, 4 Step 4: F is in lowest terms; vertical asymptote: = − x 2 Step 5: Oblique asymptote: = − y x 5, not intersected Step 6: 6 27 220 7 Step 7: y 12 x 10 (4, 0) (5, 0.86) (0, 22) (23, 214) (21.5, 5.5) (21, 0) x 5 22 y 5 x 2 5 27. Step 1: ( ) ( )( ) = + − − R x x x x 4 3 4 ; domain: { } ≠ x x 4 Step 2: R is in lowest terms Step 3: y-intercept: 3; x-intercepts: −4, 3 Step 4: R is in lowest terms; vertical asymptote: = x 4 Step 5: Oblique asymptote: = + y x 5, not intersected Step 6: 20 25 24 10 Step 7: y 21 x 10 (5, 18) (0, 3) (3, 0) (3.5, 27.5) (24, 0) 25, 2 8 9 x 5 4 y 5 x 1 5 29. Step 1: ( ) ( )( ) = + − + F x x x x 4 3 2 ; domain: { } ≠ − x x 2 Step 2: F is in lowest terms Step 3: y-intercept: −6; x-intercepts: −4, 3 Step 4: F is in lowest terms; vertical asymptote: = − x 2 Step 5: Oblique asymptote: = − y x 1, not intersected Step 6: 12 26 212 6 Step 7: y 10 x 10 (3, 0) (0, 26) (24, 0) (23, 6) 25, 2 8 3 x 5 22 y 5 x 2 1 4, 4 3 31. Step 1: Domain: { } ≠ − x x 3 Step 2: R is in lowest terms Step 3: y-intercept: 0; x-intercepts: 0, 1 Step 4: Vertical asymptote: = − x 3 Step 5: Horizontal asymptote: = y 1, not intersected Step 6: 15 215 215 15 0.01 20.5 20.01 2.5 Step 7: y 10 x 10 y 0.01 1.25 (1, 0) (1, 0) (0, 0) (0, 0) See enlarged view at right. Enlarged view x x 5 23 y 5 1 33. Step 1: ( ) ( )( ) ( )( ) = + − + − R x x x x x 4 3 2 3 ; domain: { } ≠ − ≠ x x x 2, 3 Step 2: In lowest terms, ( ) = + + R x x x 4 2 Step 3: y-intercept: 2; x-intercept: −4 Step 4: Vertical asymptote: = − x 2; hole at ( ) 3, 7 5 Step 5: Horizontal asymptote: = y 1, not intersected Step 6: 6 28 26 4 Step 7: y x 10 (0, 2) (23, 21) (24, 0) 3, 7 5 4, 4 3 25, 1 3 x 5 22 y 5 1 5
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