Free Printable PRACTICE TEST

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 vertical asymptote of the following function?

a)

x = -2

b)

x = 2

c)

y = -3

d)

y = 3

4.

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

5.

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

6.

What is the equation of the Vertical Asymptote of $y=\frac{3}{x-4}+2$

a)

$x=2$

b)

$y=2$

c)

$x=4$

d)

$y=4$

e)

No Vertical Asymptote

7.

Which is the graph of the rational equation:

a)

b)

c)

d)

8.

What are the asymptotes?

a)

x= -1& y = -3

b)

x= 1& y = -3

c)

x= -1& y =3

d)

x= 1& y=3

9.

The given graphed function would have a horizontal asymptote at

a)

x = 0

b)

y = 0

c)

x = 2

d)

y = 2

10.

Select ALL the information that applies to the given rational function.
$f\left(x\right)=\frac{x-3}{-2x^2+8x-6}$

a)

Vertical Asymptote. at x = 1

b)

No Holes

c)

Horizontal Asymptote. at y = 0

d)

y-intercept at (0, 1/2)

11.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{2x^2-2}{x^2-4x+3}$

a)

Vertical Asymptote. at x = -3 and x = 1

b)

Hole at (1, 0)

c)

Horizontal Asymptote at y = 2

d)

x-intercepts at (3,0) and (1, 0)

12.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{x^2-x}{-4x+16}$

a)

Vertical Asymptote. at x = -1

b)

No Holes

c)

Horizontal Asymptote. at y = -1/4

d)

x-intercepts at (0,0) and (-1,0)

13.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{x+3}{-3x+6}$

a)

Vertical Asymptote at x = 2

b)

No Holes

c)

Horizontal Asymptote at y = -1/3

d)

y-intercepts at (0, 1/2)

14.

Select ALL the information that applies to the given rational function. $f\left(x\right)=\frac{1}{-3x^2-9}$

a)

No Vertical Asymptote

b)

No Holes

c)

Slant (Oblique) Asymptote at $y=x-3$

d)

No x-intercept

15.

Graph the function.

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

a)

b)

c)

d)

16.

Graph the function.

$f\left(x\right)=\frac{-2x^2+2x+24}{x^3-x^2-12x}$

a)

b)

c)

d)

17.

Match the graph to the correct rational equation below.

a)

$f(x)=\frac{x^2}{x^2+x-12}$

b)

$f(x)=\frac{4x^2}{x^2-x-12}$

c)

$f(x)=\frac{2x^2-2}{2x^2}$

d)

$f(x)=\frac{x}{x^2+x-12}$

18.

Which of the following represents the graph below?

a)

b)

c)

d)

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.

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

21.

What is the domain and range?

a)

D : All real number x ≠ -3
R: All real number y≠ 1

b)

D : All real number x ≠ 1
R: All real number y≠ -3

c)

D : All real number x ≠ 3
R: All real number y≠ 1

d)

D : All real number x ≠ -1
R: All real number y≠ 3

22.

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

a)

vertical

b)

horizontal

c)

end behavior

d)

none

23.

Is there a hole or a vertical asymptote?

a)

A hole when x = 2

b)

A vertical asymptote at x = 2

c)

there is no hole or vertical asymptote

24.

Which of the following represents the graph below?

a)

b)

c)

d)

25.

What is the horizontal asymptote?

a)

x = 2

b)

x = 7

c)

y = 2

d)

y = 7

26.

Add

$\frac{2x-3}{4x-7}+\frac{2x-3}{4x-7}$

a)

$\frac{4x-6}{4x-7}\ ,\ x\ne-\frac{7}{4}$

b)

$\frac{4x^2-6x+9}{4x-7}\ ,\ \ x\ne\frac{7}{4}$

c)

$\frac{4x-6}{4x-7\ }\ ,\ x\ne\frac{7}{4}$

d)

An $\frac{4x-6}{8x-14},\ x\ne\frac{14}{8}$ swer 4

27.

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)

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

28.

Subtract

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

a)

$\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)}\ ,\ x\ne\pm\frac{2}{3}$

b)

$\frac{-2x^2-11x-3}{\left(2x-3\right)\left(2x+3\right)}\ ,\ x\ne\pm\frac{3}{2}$

c)

$\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)}\ ,\ x\ne\pm\frac{3}{2}$

d)

$\frac{-2x^2+5x+3}{\left(2x-3\right)\left(2x+3\right)}\ ,\ x\ne\pm\frac{2}{3}$

29.

Add

$\frac{2x}{x^2-36}+\frac{x+4}{x+6}$

a)

$\frac{x^2-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

b)

$\frac{x^3+6x^2-24x}{\left(x^2-36\right)\left(x+6\right)}\ x\ne-6,\ 36$

c)

$\frac{x^2+2x-24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

d)

$\frac{x^2+12x+24}{\left(x+6\right)\left(x-6\right)}\ ,\ x\ne\pm6$

30.

Add

$\frac{2}{x^2-x-20}+\frac{3}{x^2+7x+12}$

a)

$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$

b)

$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$

c)

$\frac{5x-11}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-5,\ 3,\ 4$

d)

$\frac{5x-9}{\left(x-5\right)\left(x+4\right)\left(x+3\right)}\ ,\ x\ne-4,\ -3,\ 5$

31.

Simplify (Add & Divide)

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

a)

$\frac{7x-21}{6x^2-6x}\ ,\ x\ne0,\ 1,\ 3$

b)

A $\frac{7x-21}{6x^2-6x}\ ,\ x\ne1,\ 3$

c)

$\frac{7x^2-21x}{6x^3-6x^2}\ ,\ x\ne0\ ,\ 1,\ 3$

d)

$\frac{7x^2-21x}{6x^3-6x^2}\ ,\ x\ne1,\ 3$

32.

Write a formula for the following sequence:

5, 8, 11, 14, 17...

a)

a_n = 3n + 2

b)

a_n = 8 - 5n

c)

a_n = 5(3)^n-1

d)

a_n = 5 + 3n

33.

Write a formula for the following sequence:

4, 12, 36, 108...

a)

a_n = 4(3^n-1)

b)

a_n = 4(3ⁿ)

c)

a_n = 4+3n

d)

a_n = 4(3n)

34.

What is the 100th term in the sequence a_n = 4n-12

a)

388

b)

40012

c)

-388

d)

100

35.

Given a₁= 5 and d= 2 find a₆

a)

13

b)

10

c)

15

d)

17

36.

Find the 25th term of the sequence if a₁ = 5 and d = 0.5

a)

18

b)

17

c)

15

d)

14

37.

Find a₁₈ for the following geometric sequence,

-3, 6, -12, 24,,,

a)

-37

b)

-786,432

c)

393,216

d)

258,280,326

38.

Write the explicit formula for the geometric sequence.

a)

a_n = 4(3)^n-1

b)

a_n = 3(4)^n-1

c)

a_n = -4(3)^n-1

d)

a_n = 3(-4)^n-1

39.

a)

149

b)

11,200

c)

5,600

d)

140

40.

Evaluate the geometric series below:
a₁ = -2, a_n = -1458, r = 3

a)

-2186

b)

-2408

c)

1

d)

-2703

41.

Find a₁ for each geometric series described.

S_n = –2912, r = 3, n = 6

a)

8

b)

-8

c)

2

d)

-2

42.

Write the explicit formula for the geometric sequence.

a)

a_n = 10(2)^n-1

b)

a_n = 2(10)^n-1

c)

a_n = 10(2)ⁿ

d)

a_n = 2(10)ⁿ

43.

A geometric sequence has a common ration(r) of 3 and the 8th term (a₈) is 13,122. What is the first term of the sequence (a₁)?

a)

3

b)

6

c)

18

d)

2

44.

Find the next three terms in the arithmetic sequence: -3, -8, -13, -18, ...

a)

-20, -24, -28

b)

-21, -25, -29

c)

-23, -28, -33

d)

-24, -29, -32

45.

Given an arithmetic sequence where a₃₂ = 109 and a₄₆ = 193, find a₃₁₁.

a)

295

b)

-77

c)

1860

d)

1783

46.

Find the arithmetic means in each sequence.

24,----,----,----,----,-1

a)

19, 14, 9, 4

b)

14, 19, 9, 4

c)

4,9,14,19

d)

19, 9,19,4

47.

Determine if the series converges or diverges

a)

Converges

b)

Diverges

48.

Determine if the series converges or diverges

a)

Converges

b)

Diverges

49.

Evaluate the infinite series described:

a)

-16

b)

-18

c)

3

d)

-15

50.

Evaluate the infinite series described:

a)

No Sum

b)

32/3

c)

2/3

d)

34/3

PRACTICE TEST

Total questions: 50

Worksheet time: 3hrs 48mins

Similar Resources on Wayground