MTH 95 Lesson 9 - Intro to Rational Functions and Multiplication and Division of themName:

1. Which of the following functions are classifies as “rational?”

a. n(x) =7x2 + 6

√x− 6

3− 7x7

b. t(x) =3− 7x3

7x0.7 + 6x− 6

c. m(x) =7x+ 6

7x+ 6

d. r(x) =7x2 + 6x− 63− 7x−7

e. c(x) =7x2 + 6x− 6

3 + |x|

f. h(x) =3

7x2 + 6x− 6

g. b(x) =7x2 + 6x− 6

3

h. s(x) =

√7x2 + 6x− 63− 7x7

i. a(x) =7x2 + 6x− 6

3− 7x7

2. Determine the domains of the following rational functions.

a. K(x) =5x

x− 10

b. g(x) = − 4x+ 3x2 − 3x− 40

c. F (x) =2x− 7x2 + 2x

d. p(x) =x− 8x2 + 16

1

a d

b

√ −−√√√x 7

x 7 + |x|x ss

h

3. Determine the domain and range of the following rational function’s graphs. What are theasymptotes of each?

a.

x

y

−6 −3 3 6

−6

−3

3

6

b.

x

y

−6 −3 3 6

−6

−3

3

6

c.

x

y

−6 −3 3 6

−6

−3

3

6

d.

x

y

−6 −3 3 6

−6

−3

3

6

4. The concentration of a drug in a patient’s blood stream, in milligrams per liter, can be

modeled by the function C(t) =9t

t2 + 6where t is the number of hours since the drug is

injected. Graph the function using GeoGebra. After how many hours will the drug’sconcentration be a maximum and what is this maximum? What is the concentration going toas time goes on?

2

5. Multiply and divide as appropriate.

a. − 911

· 1324

b. −109

·(−19

4

)c.

3

8÷ 8

3d.

4

25÷

(− 310

)

6. Simplify the following rational expressions, and if applicable, write the restricted domain onthe simplified expression.

a.t+ 7

(t− 10)(t+ 7)

b.(y − 3)(y − 9)

9− y

c.t− t2

t2 − 6t+ 5

d.5r2 + 8r + 3

−r + 5− 6r2

e. h(x) =x− 5

x2 + x− 30

f. g(r) =5r3 + 3r2

5r3 − 22r2 − 15r

3

999

24 4

)101010

t+ 7

( + 7)

g.y2 + 7y + 12

y − 6 ·5y − 30y + 4

h.5x2 − x− 4126x2 − 105x ·

15x− 18x225x2 − 16

i.y

y + 10÷ 5y2

j. (2r − 6)÷ (4r − 12)

k.x4

x2 + 6x÷ 1

x2 + x− 30

l.

r(r−3)2

9rr2−9

m.5yx

3y· 3y

2x3

25x5

n.xy2

7zx

10yz

4

x x3

x5yyy

y3

3335

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