Free Printable Day 49: Rationals Review

1.

Simplify.

a)

$\frac{\left(m+6\right)}{\left(m-3\right)}$

b)

$\frac{7}{m-3}$

c)

$\frac{7}{m+6}$

d)

$m+6$

2.

Simplify.

a)

$\frac{\left(x+6\right)}{\left(x-4\right)}$

b)

$\frac{\left(x+6\right)}{\left(x+4\right)}$

c)

$x+6$

d)

$\frac{\left(x+6\right)}{\left(x-5\right)}$

3.

Simplify.

a)

$\frac{1}{n-7}$

b)

$n-7$

c)

$\frac{\left(n-6\right)}{\left(n-7\right)}$

d)

$n-6$

4.

Simplify

Hint:(bottom is dif of square)

a)

$\frac{\left(x+9\right)}{\left(x-9\right)}$

b)

$\frac{1}{x-9}$

c)

$x+9$

d)

$\frac{1}{x+9}$

5.

a)

a

b)

b

c)

c

d)

d

6.

a)

a

b)

b

c)

c

d)

d

7.

a)

a

b)

b

c)

c

d)

d

8.

a)

a

b)

b

c)

c

d)

d

9.

a)

A

b)

B

c)

C

d)

D

10.

a)

A.

b)

B.

c)

C.

d)

D.

11.

Add the following rational expressions.

a)

$\frac{\left(7x+3\right)}{\left(x-5\right)\left(x+8\right)}$

b)

$\frac{\left(2x+3\right)}{\left(x-5\right)\left(x+8\right)}$

c)

$\frac{\left(2x+4\right)}{\left(x-5\right)\left(x+8\right)}$

d)

$\frac{\left(7x+4\right)}{\left(x-5\right)\left(x+8\right)}$

12.

a)

A.

b)

B.

c)

C.

d)

D.

13.

Subtract the fractions

a)

a

b)

b

c)

c

d)

d

14.

Solve for v.

a)

60

b)

-3

c)

15

d)

3

15.

Solve for v

a)

- 7/6

b)

- 9/5

c)

9/5

d)

-3

16.

Solve for r

a)

5

b)

- 5, 4

c)

- 5

d)

5, 4

17.

Solve the equation for x.

a)

7

b)

6

c)

14

d)

0

18.

Solve.

a)

x = 4.5

b)

x = -4.5

c)

x = 3

d)

x = -3

19.

What are the asymptotes?

a)

x = -3 y = 1

b)

x = 3 y = 1

c)

x = -3 y = -1

d)

x = 3 y = -1

20.

What is the Horizontal Asymptote?

a)

None

b)

y= 0

c)

y= 1

d)

y= 5/4

21.

What is the hole?

a)

(4, 0)

b)

(-4, 5/4)

c)

( 5, 10/9)

d)

(-5,10)

e)

No hole

22.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

23.

Which asymptote(s) are determined by setting the simplified denominator equal to zero?

a)

vertical

b)

horizontal

c)

slant

d)

none

24.

What is/are the x-intercepts of this graph?

a)

(-2,0) and (2,0)

b)

(-2,0)

c)

(3,0)

d)

(2,0) and (3,0

25.

What creates a hole in the graph of a rational function?

a)

Crossing the x-axis

b)

An absence of dirt.

c)

Crossing a vertical asymptote.

d)

A factor that cancels out.

26.

What is the domain and range?

a)

D : $\left(-\infty,-3\right)U\left(-3,\infty\right)$
R: $\left(-\infty,1\right)U\left(1,\infty\right)$

b)

D: $\left(-\infty,3\right)U\left(3,\infty\right)$
R: $\left(-\infty,-1\right)U\left(-1,\infty\right)$

c)

D : $\left(-\infty,3\right)U\left(3,\infty\right)$
R: $\left(-\infty,1\right)U\left(1,\infty\right)$

d)

D : $\left(-\infty,-1\right)U\left(-1,\infty\right)$
R: $\left(-\infty,3\right)U\left(3,\infty\right)$

27.

Find the coordinates of the hole.

a)

(-3, -3)

b)

(-3, 3)

c)

(3, -3)

d)

(3, 3)

28.

A rational function will have a horizontal asymptote at $y=0$ when _________. (Hint: Use BOSTON)

a)

The degree of the numerator is greater than the degree of the denominator. "Top-bigger"

b)

The degree of the numerator is equal to the degree of the denominator.

c)

The degree of the numerator is less than the degree of the denominator. "Bottom-bigger"

d)

Rational functions can never have horizontal asymptotes at y=0.

29.

What are the x and y intercepts?

a)

(4, 0) and (0, -4)

b)

(-4, 0) and (0, -4)

c)

(-4, 0) and (0, 4)

d)

(0, 0) and (0, -4)

30.

Which asymptote is determined by comparing the degree of the numerator and denominator (BOSTON)?

a)

vertical

b)

horizontal

c)

slant

d)

none

Day 49: Rationals Review - Math 3

Total questions: 30

Worksheet time: 4hrs 35mins

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