AN26 Answers: Chapter 4 4.6 Assess Your Understanding (page 255) 2. F 3. c 4. T 5. (a) { } ≠ x x 2 (b) 0 6. a 7. Step 1: Domain: { } ≠ ≠ − x x x 0, 4 Step 2: R is in lowest terms Step 3: no y-intercept; x-intercept: −1 Step 4: R is in lowest terms; vertical asymptotes: = = − x x 0, 4 Step 5: Horizontal asymptote: = y 0, intersected at ( ) −1, 0 Step 6: 4 27 24 3 Step 7: y 2.5 x 4 (21, 0) x 5 0 x 5 24 y 5 0 4 5 25, 2 2 2 2 7 , 1 2 22, 1 4 1, 2 5 9. Step 1: ( ) ( ) ( ) = + + R x x x 3 1 2 2 ; domain: { } ≠ − x x 2 Step 2: R is in lowest terms Step 3: y-intercept: 3 4 ; x-intercept: −1 Step 4: R is in lowest terms; vertical asymptote: = − x 2 Step 5: Horizontal asymptote: = y 3 2 , not intersected Step 6: 8 26 24 4 Step 7: y 5 x 5 (21, 0) (23, 3) x 5 22 y 5 2 2 3 2 , 3 2 0, 3 4 3 2 11. Step 1: ( ) ( )( ) = + − R x x x 3 2 2 ; domain: { } ≠ − ≠ x x x 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 2, 2 Step 5: Horizontal asymptote: = y 0, not intersected Step 6: 5 25 25 5 Step 7: y 2 x 5 x 5 2 x 5 22 y 5 0 23, 3 5 3, 3 5 3 4 0, 2 13. Step 1: ( )( ) ( ) ( )( ) = + + − + + − P x x x x x x x 1 1 1 1 2 2 ; domain: { } ≠ − ≠ x x x 1, 1 Step 2: P is in lowest terms Step 3: y-intercept: −1; no x-intercept Step 4: P is in lowest terms; vertical asymptotes: = − = x x 1, 1 Step 5: No horizontal or oblique asymptote Step 6: 12 24 26 4 Step 7: y 6 x 5 (0, 21) (22, 7) (2, 7) x 5 1 x 5 21 15. Step 1: ( ) ( ) ( ) ( )( ) = − + + + − H x x x x x x 1 1 3 3 2 ; domain: { } ≠ − ≠ x x x 3, 3 Step 2: H is in lowest terms Step 3: y-intercept: 1 9 ; x-intercept: 1 Step 4: H is in lowest terms; vertical asymptotes: = = − x x 3, 3 Step 5: Oblique asymptote: = y x, intersected at ( ) 1 9 , 1 9 Step 6: 12 28 212 8 Step 7: y 8 x 10 (24, 29.3) (2, 21.4) (4, 9) (1, 0) x 5 3 x 5 23 y 5 x 0, 1 9 17. Step 1: ( ) ( )( ) = + − R x x x x 3 2 2 ; domain: { } ≠ − ≠ x x 3, 2 Step 2: R is in lowest terms Step 3: y-intercept: 0; x-intercept: 0 Step 4: R is in lowest terms; vertical asymptotes: = = − x x 2, 3 Step 5: Horizontal asymptote: = y 1, intersected at ( ) 6, 1 Step 6: 6 28 26 8 Step 7: y 2 x 10 (26, 1.5) (1, 20.25) (0, 0) (3, 1.5) x 5 23 x 5 2 y 5 1 1 6 21, 2 19. Step 1: ( ) ( )( ) = + − G x x x x 2 2 ; domain: { } ≠ − ≠ x x x 2, 2 Step 2: G is in lowest terms Step 3: y-intercept: 0; x-intercept: 0 Step 4: G is in lowest terms; vertical asymptotes: = − = x x 2, 2 Step 5: Horizontal asymptote: = y 0, intersected at ( ) 0, 0 Step 6: 4 24 24 4 Step 7: y 2 x 5 (0, 0) x 5 2 x 5 22 y 5 0 21, 1 3 3 5 23, 2 3, 3 5 1 3 1, 2
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