Free Printable Asymptotes and Continuity

1.

The following function is not continuous at x = 3 because...

a)

f(3) does not exist

b)

limit from left of 3 does not equal limit from right of 3

c)

3 is not a lucky number

2.

Find the vertical asymptote(s) (if any) of the graph of the function.

a)

None

b)

x=2

c)

x=-2

d)

x=0

3.

What is the horizontal asymptote to this function?

a)

4

b)

0

4.

Which asymptotes are determined by looking at the denominator of a function?

a)

vertical

b)

horizontal

c)

slant

d)

none

5.

What are the asymptotes?

a)

x=-2 y=-1

b)

x=-2 y=1

c)

x=2 y=1

d)

x=2 y = -1

6.

Which of the following best describes the continuity at x = 5?

a)

Continuous

b)

Removable Point Discontinuity

c)

Non-removable Infinite Discontinuity

d)

Non-removable Jump Discontinuity

7.

Find the value that makes the function continuous

a)

c=1/3

b)

c=3

c)

c=-3

d)

c=-1/3

8.

a)

DNE

b)

9

c)

1

d)

0

9.

What is the horizontal asymptote to this function?

a)

x=4

b)

y=0

c)

x=0

d)

y=4

10.

What are the asymptotes?

a)

x=-2 and y=-1

b)

x=-2 and y=1

c)

x=2 and y=1

d)

x=2 and y = -1

11.

Which of the following is true?

a)

b)

c)

d)

12.

a)

I only

b)

I and II only

c)

I and III only

d)

All of these

13.

Find the point or points of discontinuity. If none, state continuous.

f\left(x\right)=\frac{5}{x-3}

a)

$x=3$ hole

b)

$x=-3$ VA

c)

$x=3$ VA

d)

Continuous

14.

Let f be the function defined above where c is a constant. For what value of c, if any is f continuous at x=c ?

a)

6

b)

8

c)

10

d)

There is no such value c

15.

Which is not an appropriate reason for the discontinuity on [-2,1]?

a)

f(-2) not defined

b)

removable discontinuity at x = -0.5

c)

$\lim_{x\rightarrow-0.5}f\left(x\right)$ does not exist

d)

$\lim_{x\rightarrow1^-}f\left(x\right)$ $\ne\ f\left(1\right)$

16.

What are the vertical asymptotes of the function f(x)=(x²-9)/(x²+6x+9)

a)

x=3

b)

x=-3

c)

x=3,-3

d)

no vertical asymptote

17.

what is the limit when x approaches infinity of the function f(x)=e^x

a)

negative infinity

b)

e

c)

infinity

d)

0

18.

Select all statements that are TRUE.

a)

b)

c)

d)

e)

19.

Which of the following statement(s) are false?

a)

f is continuous at a

b)

the limit as x approaches a exists

c)

f is differentiable at a

d)

f(a) exists

e)

None, all statements are true

20.

The function is continuous at x = a . True or false?

a)

True

b)

False

21.

a)

1

b)

Does not exist

c)

0

d)

-1

22.

What is the horizontal asymptote?

a)

y = -4

b)

y = 1

c)

x = 1

d)

y = -6

23.

in what value of x does the following function is discontinuous?

a)

3

b)

-3

c)

6

d)

-6

Asymptotes and Continuity

Total questions: 23

Worksheet time: 42mins

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