Free Printable A2 Rational Functions Review

1.

How is this function transformed from the parent function?

a)

Translated left and up

b)

Translated right and up

c)

Translated left and down

d)

Translated right and down

2.

Which asymptote(s) are determined by looking at the denominator?

a)

vertical

b)

horizontal

c)

end behavior

d)

none

3.

What are the asymptotes?

a)

x=-3, y=1

b)

x=3, y =1

c)

x=-3, y =-1

d)

x=3 y=-1

4.

What is the horizontal asymptote of the function?

a)

y=0

b)

none

c)

y=1

5.

Describe all transformations from the parent function g(x)=1/x to f(x).

a)

Shift right 5 and shift up 7

b)

Shift left 7 and shift up 5

c)

Reflect over the x-axis, shift up 7

d)

Shift left 5 and shift up 7

6.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

7.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

8.

Find the hole of the function.
3x²+ 21x
_________
x²+5x-14

a)

x =2,-7

b)

x=7

c)

x=-7

d)

x=-4,3

9.

Find the vertical asymptote.
3x²+ 21x
_________
x²+5x-14

a)

y=2

b)

x=3/2

c)

x= 2

d)

x=7

10.

Find the horizontal asymptote.

a)

None

b)

y = 0

c)

y = -1/3

d)

y = -3

11.

Describe all transformations from the parent function g(x)=1/x to f(x).

a)

Shift right 5 and shift up 7

b)

Shift left 7 and shift up 5

c)

Reflect over the x-axis, shift up 7

d)

Shift left 5 and shift up 7

12.

What is the domain?

a)

x≠ -5,5

b)

x≠ -5,4

c)

x≠ -4,5

d)

x≠ -4,-5

13.

Find the horizontal asymptote.
4x-16
_________
x²-16

a)

y=2

b)

y=1

c)

y=0

d)

none

14.

Find the hole of the function.
x²- 9x+20
___________
4x² - 12x- 40

a)

x =5

b)

x=0

c)

x=4

d)

x=-2

15.

Find the hole of the function.
3x²+ 21x
_________
x²+5x-14

a)

x =2,-7

b)

x=7

c)

x=-7

d)

x=-4,3

16.

Which of the following represent the graph?

a)

b)

c)

d)

17.

Describe the transformations from the parent function g(x) =1/x

a)

reflection over the x-axis, right 2, down 4

b)

reflection over the y-axis, right 2 down 4

c)

reflection over the x-axis, left 2, down 4

d)

reflection over the y-axis, left 2, down 4

18.

The horizontal asymptote equals zero when:

a)

the exponents in the numerator and denominator are equal

b)

the exponents in the denominator are greater than the numerator

c)

the exponents in the numerator are greater than the denominator

d)

the numerator equals zero

19.

The holes of a rational function occur when :

a)

my pencil pokes a hole in the paper I'm working on

b)

there is something left in the denominator

c)

the value of f(0)

d)

a factor in the denominator cancels with a factor in the numerator

20.

Describe the transformation.

a)

Reflect over x-axis, left 3, up 3

b)

Reflect over x-axis, right 3, up 3

c)

Reflect over y-axis, left 3, up 3

d)

Reflect over x-axis, right 3, down 3

21.

Describe the transformation

a)

vertical stretch by a factor of 2, left 2, up 2

b)

vertical stretch by a factor of 2, right 2, up 2

c)

vertical stretch by a factor of 2, right 2, down 2

d)

vertical compression by a factor of 2, right 2, down 2

22.

Describe the transformation.

a)

vertical compression by a factor of 2, reflect over x-axis, right 1, down 4

b)

vertical compression by a factor of .5, reflect over x-axis, left 1, down 4

c)

vertical stretch by a factor of .5, left 1, up 4

d)

vertical stretch by a factor of .5, reflect over x-axis, left 1, down 4

23.

Find the holes.

a)

None

b)

x = -1

c)

x = 2, 5

d)

x = 3

24.

Find all holes.

a)

None

b)

x = -4

c)

x = 0

d)

x = 1, 4

25.

Identify the LCD.

a)

x²(x - 2)

b)

x(x - 2)

c)

x

d)

(x - 2)

26.

Solve by using the LCD.

a)

x = 1

b)

x = 2, 4

c)

x = 0, 5

d)

x = -5, -1

27.

Solve by using the LCD.

a)

x = 1

b)

x = -3

c)

x = 0

d)

x = 3

28.

Solve for x

a)

5/3, 1

b)

- 5, 1

c)

5, 2/3

d)

5, 1

29.

Solve for n

a)

- 2, - 1

b)

- 5, - 1

c)

- 2

d)

- 2, - 2/3

30.

a)

b)

c)

d)

31.

Add
$\frac{3x-2}{x+2}+\frac{2x}{4x-1}$

a)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$

b)

$\frac{14x^2-9x-2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ 1$

c)

$\frac{12x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-2,\ \frac{1}{4}$

d)

$\frac{14x^2-7x+2}{\left(x+2\right)\left(4x-1\right)};\ x\ne-\frac{1}{4},\ 2$

32.

Subtract
$\frac{6}{x^2+4x-32}-\frac{x-5}{x-4}$

a)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)};\ x\ne-8,\ 4$

b)

$\frac{-x^2+3x-34}{\left(x+8\right)\left(x-4\right)};\ x\ne-4,\ 8$

c)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)};\ x\ne-8,\ 4$

d)

$\frac{-x^2-3x+46}{\left(x+8\right)\left(x-4\right)};\ x\ne-4,\ 8$

33.

a)

a

b)

b

c)

c

d)

d

34.

a)

a

b)

b

c)

c

d)

d

35.

a)

a

b)

b

c)

c

d)

d

36.

Simplify.

a)

(x+6)/(x+4)

b)

(x+6)(x+4)

c)

(x+6)

d)

(x+6)/(x-5)

37.

(-x-5)/(x²+12x+35)

a)

A. 1/(x+7)

b)

B. 1/(x-7)

c)

C. -1/(x+7)

d)

D. -1/(x+6)

38.

$\frac{b-4}{b^2-14b+40}\div\frac{b^2+6b+8}{b^2-3b-70}$

a)

$\frac{b-3}{6}$

b)

$\frac{2b}{9}$

c)

$\frac{5b\left(b-6\right)}{7}$

d)

$\frac{b+7}{\left(b+4\right)\left(b+2\right)}$

39.

Divide the Rational Expression
$\frac{x^2-4x-5}{x^2-3x+2}\div\frac{x^2-3x-10}{x^2-4}$

a)

$\frac{x-5}{x-1}$

b)

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

c)

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

d)

$x+1$

40.

Factor and cancel out in order to simplify.

a)

1/(n-7)

b)

n-7

c)

(n-6)/(n-7)

d)

n-6

A2 Rational Functions Review

Total questions: 40

Worksheet time: 2hrs 42mins

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