date: 5.0 worksheet (2...
TRANSCRIPT
Name:_______________ Date:_______________
5.0 Worksheet (2 pages) Simplify the following Rational Expressionsโฆ.make sure answers are in FACTORED FORM.
1. ๐๐(๐+๐)
๐๐๐ 2.
(๐+๐)(๐โ๐)
๐+๐ 3.
๐โ๐
๐โ๐
4. ๐+๐
๐+๐ 5.
๐๐(๐๐โ๐)
๐๐(๐๐โ๐) 6.
๐(๐โ๐)
๐๐
7. ๐(๐โ๐)
๐๐+๐ 8.
โ๐๐๐๐๐(๐โ๐)
๐๐๐๐(๐โ๐) 9.
๐๐โ๐
๐๐โ๐๐+๐
10. ๐๐๐+๐๐+๐
๐๐๐โ๐๐โ๐ 11.
๐๐โ๐๐
๐โ๐ 12.
๐๐๐+๐๐โ๐
๐๐โ๐โ๐
Name:_______________ Date:_______________
Multiplying and Dividing Rational Expressionsโฆmake sure answers are in FACTORED FORM.
13. ๐๐๐๐๐
๐๐๐โ๐๐๐
๐๐๐ 14.
๐โ๐
๐โ๐โ๐๐โ๐
๐โ๐ 15.
๐๐โ๐๐
๐๐+๐โ
๐+๐
๐๐+๐๐+๐๐
16. ๐๐โ๐๐+๐
๐โ
๐
(๐โ๐)๐ 17.
๐๐๐๐
๐๐๐โ๐๐๐๐
๐๐๐ 18.
๐๐๐๐
๐โ
๐
๐๐๐๐
19. ๐๐โ๐๐
๐๐โ๐๐รท
๐+๐
๐โ๐ 20.
๐๐๐โ๐๐๐
๐๐๐+๐๐โ๐รท
๐๐๐
๐๐๐โ๐ 21.
๐๐โ๐๐+๐
๐รท
๐โ๐
๐๐
22. ๐๐+๐
๐๐+๐๐รท
๐๐โ๐
๐๐โ๐ 23.
๐๐โ๐๐
๐๐+๐รท
๐๐โ๐๐โ๐
๐๐โ๐โ๐ 24.
๐๐ โ ๐๐
๐๐ + ๐๐โ๐๐ + ๐๐ + ๐
๐๐ โ ๐๐รท
๐ + ๐
๐๐ + ๐๐
Name:_______________ Date:_______________
5.1 Worksheet (2 pages) Find the SUM or DIFFERENCE.
a. ๐ฅ2+3๐ฅ
๐ฅ+2+
2๐ฅ+6
๐ฅ+2 b.
7๐ฅ+3
๐ฅ2โ1โ
6
๐ฅโ1
c. 7๐ฅ+3
๐ฅ2โ1โ
6๐ฅ+4
๐ฅ2โ1
d. 6๐ฆ+13
๐ฆ2โ4๐ฆโ21โ
๐ฆโ2
๐ฆ2โ4๐ฆโ21
e. 4๐ฅ
๐ฅ2+9๐ฅ+18+
5
๐ฅ+6
f. 3๐+6
๐2โ16โ
7
6๐+24
Name:_______________ Date:_______________
Simplify Each Complex Fraction.
g.
1
๐ฆ2โ1
1+1
๐ฆ
h. 25
๐โ๐
5+๐
i. 4+
12
2๐ฅโ3
5+15
2๐ฅโ3
j. ๐ฅ
3๐ฅโ2๐ฅ
9๐ฅ2โ4
Name:_______________ Date:_______________
5.2 Worksheet (2 pages) Solve each Rational Equation. Make sure to include all restrictions on Domain and
Check solutions for any extraneous solutions.
1. 1
6๐2=
1
3๐2โ
1
๐ 2.
๐+6
4๐2+
3
2๐2=
๐+4
2๐2 3.
1
๐ฅ=
6
5๐ฅ+ 1
4. 1
๐ฃ+
3๐ฃ+12
๐ฃ2โ5๐ฃ=
7๐ฃโ56
๐ฃ2โ5๐ฃ 5.
1
๐2โ๐+
1
๐=
5
๐2โ๐ 6.
1
๐โ8โ 1 =
7
๐โ8
7. 1
๐โ2+
1
๐2โ7๐+10=
6
๐โ2 8. 1 =
๐ฃ+2
๐ฃโ4+
7๐ฃโ42
๐ฃโ4 9.
๐โ4
5๐=
1
5๐+ 1
Name:_______________ Date:_______________
10. 1 +๐ฅ2โ5๐ฅโ24
3๐ฅ=
๐ฅโ6
3๐ฅ
11. 1 =1
๐ฅ2+2๐ฅ+
๐ฅโ1
๐ฅ
12. ๐+5
๐+8= 1 +
6
๐+1 13.
๐+5
๐2โ2๐โ 1 =
1
๐2โ2๐
14. ๐โ2
๐+3โ 1 =
3
๐+2 15.
5
๐3+2๐2=
4
๐+2+
1
๐2
Name:_______________ Date:_______________
5.3 Worksheet (2 pages) Given the following Rational Functions. Identify the asymptotes, domain, and range of each function.
a) ๐(๐) =๐
๐+๐ b) ๐(๐) =
๐
๐โ ๐
c) ๐(๐) =๐
๐+๐โ ๐ d) ๐(๐) =
โ๐
๐โ๐+ ๐
e) ๐(๐) =๐
๐ f) ๐(๐) =
โ๐
๐โ๐+ ๐
g) ๐(๐) =๐
๐๐โ๐ h) ๐(๐) =
๐
๐๐+๐โ ๐
Name:_______________ Date:_______________
Graph each function. State the Domain and Range.
i) ๐(๐) =๐
๐โ๐โ ๐
j) ๐(๐) =โ๐
๐+๐โ ๐
k) ๐(๐) =๐
๐โ ๐
l) ๐(๐) =โ๐
๐
๐๐โ๐
+ ๐
Name:_______________ Date:_______________
5.4 Worksheet (1 page) For the following Functions, find (if they apply to the function):
a) the vertical asymptote(s)
b) the horiztonal/slant asymptotes
c) the holes
1. ๐(๐ฅ) =2๐ฅ
๐ฅ2โ1 2. ๐(๐ฅ) =
๐ฅ2โ5๐ฅ+6
๐ฅ2โ4๐ฅ+3
3. ๐(๐ฅ) =8
๐ฅ2โ๐ฅโ6 4. ๐(๐ฅ) =
๐ฅ2+11๐ฅ+18
2๐ฅ+1
5. โ(๐ฅ) =๐ฅ2โ9
2๐ฅ2+1 6. ๐(๐ฅ) =
๐ฅโ4
๐ฅ2โ3๐ฅ
Name:_______________ Date:_______________
5.5 Worksheet (2 pages) For the following Functions, find (if they apply to the function):
a) the ๐-intercepts, and ๐-intercepts
b) the vertical asymptote(s)
c) the horiztonal/slant asymptotes
d) the holes
e) any additional points needed
f) then, graph each function
7. ๐(๐ฅ) =2๐ฅ
๐ฅ2โ1
8. ๐(๐ฅ) =๐ฅ2โ5๐ฅ+6
๐ฅ2โ4๐ฅ+3
Name:_______________ Date:_______________
9. ๐(๐ฅ) =8
๐ฅ2โ๐ฅโ6
10. ๐(๐ฅ) =๐ฅ2+11๐ฅ+18
2๐ฅ+1
11. โ(๐ฅ) =๐ฅ2โ9
2๐ฅ2+1
12. ๐(๐ฅ) =๐ฅโ4
๐ฅ2โ3๐ฅ
Name:_______________ Date:_______________
5.6 Worksheet (2 pages) Solve Each Rational Inequality. Write answers in interval notation.
1. 3 โ4
๐ฅ>
5
4๐ฅ 2.
5
3๐โ
3
4๐>
5
6
3. ๐ฅโ2
๐ฅ+2+
1
๐ฅโ2>
๐ฅโ4
๐ฅโ2 4.
3
4โ
1
๐ฅโ3>
๐ฅ
๐ฅ+4