Free Printable Unit 8 Rational Functions

1.

$Simplify:\ \frac{5a^3c^{10}}{20a^5c^4}$

a)

$\frac{4c^6}{a^2}$

b)

$\frac{1a^2c^6}{4}$

c)

$\frac{1c^6}{4a^2}$

d)

$\frac{1a^2}{4c^6}$

2.

$Simplify:\ \ \frac{x^2+6x}{x^2+3x-18}$

a)

$\frac{x}{x+3}$

b)

$\frac{x}{x-3}$

c)

$\frac{x+6}{x-3}$

d)

$\frac{x}{x+6}$

3.

Simplify

a)

A. $\frac{4x^3}{\left(x+2\right)}$

b)

B. $\frac{4x³}{(x+10)}$

c)

C. $\frac{2x³}{(5x+1)}$

d)

D. $\frac{4x^3}{\left(x-2\right)}$

4.

Find the least common denominator of the expression

a)

18

b)

6x

c)

3xy

d)

6xy

5.

a)

A

b)

B

c)

C

d)

D

6.

Divide the Rational Expression

a)

A

b)

B

c)

C

d)

D

7.

Divide the Rational Expression

a)

1/6

b)

x+10/ 6x+60

c)

x+8/ 6x+60

d)

(x+10)(x+8)/ 6x+60

8.

$\frac{x+\frac{3}{x^2}}{1-\frac{2}{x}}$

a)

$\frac{x^3+3}{x^2-2x}$

b)

$\frac{x\left(x+3\right)}{x-2}$

c)

$\frac{x+3}{x-2}$

d)

$\frac{x\left(x^3+3\right)}{x-2}$

9.

$\frac{\frac{x+1}{x+4}-\frac{1}{x}}{x+1}$

a)

$\frac{x^2+x}{4-x^2}$

b)

$\frac{x^3+5x^2+4x}{x^2+2x+4}$

c)

$\frac{x^2-4}{x^3+5x^2+4x}$

d)

$\frac{x^3+9x^2+24x+16}{2x^4+9x^3+16x^2}$

10.

$\frac{\frac{4}{x-2}-\frac{x}{16}}{\frac{x^2}{2x-4}+\frac{x-2}{4}}$

a)

$\frac{x-2}{x-6}$

b)

$\frac{64-x^2+2x}{12x^2-16x+16}$

c)

$\frac{12x-32+2x^2}{66x-x^2}$

d)

$\frac{20x-24x-4x^2}{x+30}$

11.

$\frac{6}{x-3}-\frac{1}{x^2+3x-18}=\frac{1}{x-3}$

a)

$\frac{5}{29}$

b)

$-\frac{29}{5}$

c)

$\frac{29}{5}$

d)

3

12.

Which of the following represents the graph below?

a)

b)

c)

d)

13.

What is the domain for the following function?

a)

All real numbers except 2.

b)

All real number except -2.

c)

All real numbers except 4.

d)

All real numbers.

14.

Describe the transformations of the function.

a)

Shifted right by 4 units

Shifted down by 7 units

Stretched Vertically

b)

Shifted right by 4 units

Shifted up by 7 units

Stretched Vertically

c)

Shifted right by 4 units

Shifted down by 7 units

Compressed Vertically

d)

Shifted left by 4 units

Shifted down by 7 units

Compressed Vertically

15.

What is the horizontal asymptote of the function?

a)

x =1

b)

x = -2

c)

x = 2

d)

y = 0

16.

What's the vertical asymptote of the function?

a)

x = 5

b)

x = 0

c)

x =5 , x = -5

d)

x = 25

17.

What's the vertical asymptote of the function?

a)

x = -4, x = 1

b)

x = 4, x = -1

c)

x = -4, x = -1

d)

x = 4, x = 1

18.

What is the X-Intercept?

a)

x= 0

b)

x= 4

c)

x= 5

d)

x= -5

19.

What are the x-intercepts?

a)

x= 2/3

b)

x= 4, x = -2

c)

x= -8, x = 1

d)

x= -4, x = 2

20.

Find the horizontal asymptote:

a)

y = 0

b)

y = 1

c)

None

d)

y = 3/2

21.

What is the domain?

a)

x≠ -5,5

b)

x≠ -5,4

c)

x≠ -4,5

d)

x≠ -4,-5

22.

How do you find the y-intercept?

a)

replace all x-values with 0

b)

replace all y-values with 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

23.

How do you determine the Horizontal Asymptote?

a)

replace all x-values with 0

b)

replace the y-value with 0 or make the numerator equal 0

c)

set denominator equal to 0

d)

compare the degrees of the numerator and denominator

24.

Find the horizontal asymptote.

a)

None

b)

y=-2

c)

y=2

d)

y=0

25.

Graph the function.

$f\left(x\right)=\frac{-x+1}{x-4}$

a)

b)

c)

d)

26.

What is the horizontal asymptote of this function?

a)

y=2

b)

x=1/2

c)

y=1

d)

y=1/2

27.

What (if any) holes exist?

a)

x=2

b)

x=2 and x=3

c)

x=-3

d)

x=3

28.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

29.

Match the graph to the correct rational equation below.

a)

f(x)=x²/(x²+x-12)

b)

f(x)=4x²/(x²-x-12)

c)

f(x)=(2x²-2)/2x²

d)

f(x)=x/(x²+x-12)

30.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

31.

Solve for x

a)

x = 10

b)

x = -30/13

c)

x = 6

d)

no solution

32.

Solve for y $\frac{y+2}{3}-\frac{y-1}{4}=\frac{2}{3}$

a)

y = -9

b)

y = -3

c)

y=1

d)

y = 3

33.

$\frac{2n+16}{n-8}=\frac{1}{2n-16}-\frac{1}{2}$

a)

$-\frac{23}{5}$

b)

$7$

c)

$-4$

d)

$\frac{4}{3}$

34.

Solve: $\frac{3}{x-5}-\frac{20}{x^2-25}=\frac{2}{x+5}$

a)

$x=-5$

b)

$x=5$

c)

$\frac{5}{\left(x+5\right)\left(x-5\right)}$

d)

No Solution

35.

The number of hours to paint a house varies inversely with the number of painters working. A 2400-square foot house can be painted in 27 hours by 6 painters. How many painters would need to work in order to paint the house in 18 hours?

a)

8 painters

b)

10 painters

c)

9 painters

d)

11 painters

36.

The time it takes to fly from Los Angeles to New York varies inversely as the speed of the plane. If the trip takes 6 hours at 900 km/h, how long would it take at 800 km/h?

a)

5.33 hours

b)

6.75 hours

c)

12 hours

d)

10 hours

37.

The gas pressure in a chamber varies directly with the temperature in the chamber. If the pressure in the chamber is 150 atmospheres (atm) when the chamber is at 50 degrees, what is the pressure in the chamber when the temperature of the chamber is 75 degrees?

a)

175 atm

b)

200 atm

c)

225 atm

d)

275 atm

38.

The equation
xy = 25 represents:

a)

direct variation

b)

inverse variation

c)

joint variation

d)

none of these

39.

Determine the type of variation:

a)

Direct

b)

Inverse

c)

Neither

40.

The number of minutes needed to solve an exercise set of variation problems varies directly as the number of problems and inversely as the number of people working on the solutions. It takes 4 people 36 minutes to solve 18 problems. How many minutes will it take 6 people to solve 42 problems.

a)

56 minutes

b)

52 minutes

c)

48 minutes

d)

44 minutes

41.

z varies inversely with x and directly with y. If x = 1/2, y = 5 and z = 20, find x when z = -4 and y = 8.

a)

1

b)

2

c)

3

d)

4

42.

Write the given statement in a mathematical equation.

Interest (I) varies jointly as the principal (P) amount deposited, and the rate (r) and time (t) of the deposit.

a)

I = kPrt

b)

P = kIrt

c)

T = kPIt

d)

r = kPIt

43.

z varies jointly with x and y. If x = 7, y = 3 and z = -14, find y when z = -8 and x = 3.

a)

3

b)

4

c)

5

d)

6

Unit 8 Rational Functions

Total questions: 43

Worksheet time: 2hrs 44mins

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