Analysis worksheet - Math For Life | Mrs. W. Young (WHS ...
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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