Quiz about Rationals Discontinuity and Asymptotes

Question 1

Determine the vertical asymptote(s) for the following function.

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

Accepted Answer

x = 5

Answer

x = -3

Answer

x = -3 and x = 5

Answer

x = 0

Answer

Does Not Exist

Question 2

Determine the vertical asymptote(s) for the following function.

$$f\left(x\right)=\frac{2x}{x-7}$$

Accepted Answer

x = 7

Answer

x = 0

Answer

x = 2

Answer

x = -7

Answer

Does Not Exist

Question 3

Determine the horizontal asymptote(s) for the following function.

$$f\left(x\right)=\frac{2x^3+5x-1}{4x^3-2x^2}$$

Accepted Answer

y = 1/2

Answer

y = 0

Answer

y = 2

Answer

y = 4

Answer

Does Not Exist

Question 4

Determine the horizontal asymptote(s) for the following function.

$$f\left(x\right)=\frac{2x-5}{x^2-1}$$

Accepted Answer

y = 0

Answer

y = 2

Answer

y = 1

Answer

y = -1

Answer

Does Not Exist

Question 5

Determine whether the graph of the function has a vertical asymptote or a removeable discontinuity at x = -1.

Accepted Answer

Vertical Asymptote

Answer

Discontinuity

Answer

Bob, bob, bob

Answer

Infinite

Question 6

Where are the discontinuities?

Accepted Answer

holes: x=5

asymptotes: x=3

Answer

holes: x=3

asymptotes: x=5

Answer

holes: x=-5

asymptotes: x=-3

Answer

holes: x=-3

asymptotes: x=-5

Question 7

Where are the discontinuities?

Accepted Answer

holes: x=-1

asymptotes: none

Answer

holes: x=-3

asymptotes: x=-1

Answer

holes: none

asymptotes: x=-1

Answer

holes: x=-1

asymptotes: x=-3

Question 8

This equation has 2 discontinuities. Are they . . . . . .?

Accepted Answer

Both non-removable.

Asymptotes.

Answer

Both removable.

Holes.

Answer

One is removable. One is non-removable.

An asymptote and a hole.

Answer

There is only one discontinuity.

Question 9

State the x-values where there is a discontinuity. Label them as removable or non-removable.

Accepted Answer

x = 0, non-removable

Accepted Answer

x = 7, removable

Answer

x = 7, non-removable

Answer

x = 0, removable

Answer

x = 3, non-removable

Question 10

Identify the points of discontinuity, holes, vertical asymptotes, zeros, horizontal asymptotes, and domain for the following function: $$f\left(x\right)=\frac{-x^2-4x}{x^2+x}$$

Accepted Answer

Question 11

Describe the discontinuities

Accepted Answer

one removable discontinuity and one infinite discontinuity

Answer

two infinite discontinuities

Answer

one removable discontinuity

Answer

one removable discontinuity and one iump discontinuity

Question 12

In what value of x will the following function discontinuous?

Accepted Answer

-2

Answer

-1

Answer

-3

Answer

-4

Question 13

Choose the correct statement about the discontinuities of f(x).

Accepted Answer

one removable and one non-removable discontinuity

Answer

one removable discontinuity

Answer

two non-removable discontinuities

Answer

one non-removable discontinuity

Answer

one removable and two non-removable discontinuities

Question 14

$$\frac{x^2-8x-20}{x-10}$$

This equation has 1 discontinuity. It is . . . . . .?

Accepted Answer

Removable.

Hole.

Answer

Non-removable.

Asymptote.

Answer

Both.

An asymptote and a hole.

Answer

Neither

We haven't covered this.

Answer

There is no discontinuity.

Question 15

Determine all removable points of discontinuity (holes), vertical asympotes, and horizontal asympotes for the following function.

$$f\left(x\right)=\frac{2x-1}{2x^2+5x-3}$$

Accepted Answer

Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 0

Answer

Holes: x = -3
Vertical: x = 1/2
Horizontal: y = 0

Answer

Holes: Do Not Exist
Vertical: x = 1/2 and x = -4
Horizontal: y = 1

Answer

Holes: x = 1/2
Vertical: x = -3
Horizontal: y = 1

Answer

Holes: x = -3
Vertical: x = 1/2
Horizontal: Does Not Exist

Question 16

Identify the points of discontinuity, holes, vertical asymptotes, zeros, horizontal asymptotes, and domain for the following function: $$f\left(x\right)=-\frac{3}{x+2}$$

Accepted Answer

Rationals Discontinuity and Asymptotes

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