Free Printable Lesson 8.2 Review

1.

Which of the following represents the graph below?

a)

b)

c)

d)

2.

Which of the following represent the graph?

a)

b)

c)

d)

3.

What is the domain for the following function?

a)

$\left(-\infty,2\right)U\left(2,\infty\right)$

b)

$\left(-\infty,-2\right)U\left(-2,\infty\right)$

c)

$\left(-\infty,4\right)U\left(4,\infty\right)$

d)

$\left(-\infty,-4\right)U\left(-4,\infty\right)$

4.

What is the vertical asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

5.

What is the horizontal asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

6.

Describe the transformation of the function.

a)

shift left 3 units

b)

shift right 3 units

c)

shift up 3 units

d)

shift down 3 units

7.

Describe the transformation of the function.

a)

shift right by 3 units

b)

shift left by 3 units

c)

shift up by 3 units

d)

shift down by 3 units

8.

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

9.

Describe the transformations of the function.

a)

Shift up by 2 units

Reflected over the x-axis

b)

Shift down by 2 units

Reflected over the y-axis

c)

Shift up by 2 units

Reflected over the y-axis

d)

Shift left by 2 units

Reflected over the x-axis

10.

What is the vertical asymptote of the function?

a)

x = 2

b)

x = -2

c)

x = 0

d)

x = 1

11.

What is the horizontal asymptote of the function?

a)

x =1

b)

x = -2

c)

x = 2

d)

y = 0

12.

What is the vertical asymptote of the function?

a)

x = 7

b)

x = -7

c)

x = 6

d)

x = -6

13.

What is the horizontal asymptote of the function?

a)

y = 7

b)

y = -7

c)

y = 6

d)

y = -6

14.

What is the range for the following function?

a)

$\left(-\infty,2\right)U\left(2,\infty\right)$

b)

$\left(-\infty,-2\right)U\left(-2,\infty\right)$

c)

$\left(-\infty,4\right)U\left(4,\infty\right)$

d)

$\left(-\infty,-4\right)U\left(-4,\infty\right)$

15.

Referring to f(x) = $\frac{1}{x}$ which function shifts right 10 units and down 4 units?

a)

F(x) = $\frac{1}{x-10}-4$

b)

F(x) = $\frac{1}{x+10}+4$

c)

F(x) = $\frac{1}{x-4}+10$

d)

F(x) = $\frac{1}{x+4}-10$

16.

a)

$\left(-\infty,\ \infty\right)$

b)

$\left(-\infty,\ 0\right)U\left(0,\ \infty\right)$

c)

$\left(-\infty,\ -2\right)U\left(-2,\ \infty\right)$

d)

$\left(-\infty,\infty\right)U\left(\infty,\ \infty\right)$

17.

Which graph represents the function?

f\left(x\right)=\frac{1}{x-4}+3

a)

b)

c)

d)

18.

What are the asymptotes?

a)

x=-1 y = -3

b)

x=1 y = -3

c)

x=-1 y =3

d)

x=1, y=3

19.

Which is the graph of the rational equation:

a)

b)

c)

d)

20.

What is the vertical asymptote?

a)

x = 2

b)

y = 2

c)

x = 1

d)

y = 1

21.

What is an asymptote?

a)

an imaginary line that your function never touches

b)

a part of your function

c)

a point on your graph

d)

a type of fruit

22.

What is the domain and range?

a)

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

b)

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

c)

D : $\left(-\infty,3\right)\cup\left(3,\infty\right)$
R: undefined

d)

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

23.

What is the domain and range?

a)

D:\ \left(-\infty,2\right)\cup\left(2,\infty\right)

R:\ \left(-\infty,1\right)\cup\left(1,\infty\right)

b)

$D:\ \left(-\infty,1\right)\cup\left(1,\infty\right)$
$R:\ \left(-\infty,2\right)\cup\left(2,\infty\right)$

c)

$null$
$R:\ \left(-\infty,\frac{1}{2}\right)\cup\left(\frac{1}{2},\infty\right)$

d)

$D:\ \left(-\infty,-2\right)\cup\left(-2,\infty\right)$
$R:\ \left(-\infty,-1\right)\cup\left(-1,\infty\right)$

24.

What is the vertical asymptote?

a)

x =-3

b)

y = -3

c)

x = 3

d)

y = 3

25.

What is the horizontal asymptote?

a)

x = 2

b)

y = 2

c)

x =-2

d)

y=-2

26.

Identify the transformation(s) from the parent function f(x)=1/x: $f\left(x\right)=\frac{5}{x}$

a)

Shifted up by 5

b)

Stretched by a factor of 5

c)

Compressed by a factor of 5

d)

Shifted right by 5

27.

Write the equation of the rational function that has been reflected over the x-axis and translated 4 units right: $y=\frac{2}{x}$

a)

$y=-\frac{2}{x+4}$

b)

$y=\frac{2}{x-4}$

c)

$y=-\frac{2}{x-4}$

d)

$y=-\frac{2}{x}+4$

28.

Write the equation for the function that has been translated 2 units left and 5 units down: $y=\frac{3}{x}$

a)

$y=\frac{3}{x+2}-5$

b)

$y=\frac{3}{x-2}-5$

c)

$y=\frac{3}{x-5}+2$

d)

$y=\frac{3}{x+5}+2$

29.

Factor
x²+ 9x - 36

a)

(x + 12)(x - 3)

b)

(x + 9)(x - 4)

c)

(x - 12)(x + 3)

d)

(x - 9)(x - 4)

30.

Factor:

5x³- 7x²

a)

x²(5x - 7)

b)

x(5x²- 7x)

c)

x³(5 - 7x)

d)

Prime

31.

Factor: 25x²- 9

a)

(5x + 3)(5x - 3)

b)

(x + 5)(x - 3)

c)

(x - 3)(x + 5)

d)

(5x + 3)(3x + 5)

32.

Factor:
x² + 5x - 24

a)

(x - 8)(x + 3)

b)

(x + 8)(x - 3)

c)

(x + 6)(x - 4)

d)

(x + 12)(x - 2)

33.

Factor:
24c⁵ - 12c³

a)

6(4c⁵ - 2c³)

b)

12c³(2c²)

c)

12c³(2c² - 1)

d)

12c³(2c² - 0)

34.

Factor:
2x² - 7x + 6

a)

(x -1)(2x - 6)

b)

(x - 3) (2x - 2)

c)

(x - 2) (2x - 3)

d)

(x - 6) (2x - 1)

35.

Factor:
4n²-17n-15

a)

(n-10)(6n+1)

b)

(4n-5)(n-3)

c)

(n-5)(4n-3)

d)

(n-5)(4n+3)

36.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

Lesson 8.2 Review

Total questions: 36

Worksheet time: 2hrs 40mins

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