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Accel Math III WS Rational Functions Review

I. Combinations of functions including addition, subtraction, multiplication, division, composition. Be able to state domain and range of these functions.

1. Let [pic], [pic], and [pic]. Find

a. [pic] b. [pic] c. [pic]

III. Determine if a function is odd, even, or neither.

3. [pic]

IV. Graph rational functions, including finding domain, range, asymptotes, points of discontinuity, intercepts.

4. [pic] 5. [pic]

6. [pic]

V. Find and graph the inverse of a rational function, including finding domain and range.

7. [pic]

Accel Math III WS Rational Functions Review

VI. Add, subtract, multiply and divide rational expressions

8. [pic] 9. [pic]

10. [pic]

VII. Solve rational equations and inequalities

11. [pic] 12. [pic]

13. [pic]

VIII. Decompose into partial fractions. TB p 693 #17-22

Accel Math III WS Rational Functions Review

Answers:

I. 1a) -7 1b) 5 1c) 23

II. 2) [pic] and [pic]

III. 3) Neither

IV. 4) [pic]; [pic]; v.a.:[pic]; h.a.:[pic];

s.a.: none; point of discontinuity: [pic]; increasing: none;

decreasing: [pic]; x-int: none; y-int: [pic]

5) [pic]; [pic]; v.a.: [pic]; h.a.:[pic];

s.a.: none; point of discontinuity: [pic];

increasing: [pic]; decreasing: none;

x-int: -4; y-int: [pic]

6) [pic]; [pic];

v.a.: none; h.a.: none; s.a.: none;

point of discontinuity: [pic] and [pic];

increasing: [pic]; decreasing: none;

x-int: 2; y-int: -2

Accel Math III WS Rational Functions Review

V. 7) Inverse: [pic]

Limit original domain to [pic], then:

Inverse: [pic]; [pic]; [pic]; v.a.: none; h.a.: [pic]; s.a.: none; point of discontinuity: none; increasing: [pic]; decreasing: none; x-int: [pic]; y-int: 3

Limit original domain to [pic], then:

Inverse: [pic]; [pic]; [pic]; v.a.: none; h.a.: [pic]; s.a.: none; point of discontinuity: none; increasing: [pic]; decreasing: none; x-int: none; y-int: -3

VI. 8) [pic] 9) [pic] 10) [pic]

VII. 11) [pic] 12) [pic] 13) [pic]

VIII. 18) [pic] 20) [pic] 22) [pic]

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