Review on Limits and Continuity

Multiple Choice

Which is the graph of the rational equation:

Multiple Choice

What is the horizontal asymptote?

• x = 2

• x = 7

• y = 2

• y = 7

Multiple Choice

What is the horizontal asymptote of the function given?

• y = 2

• x = 1

• x = 2

• y = 1

Multiple Choice

what is the equation that best matches the graph?

• A

• B

• C

• D

• these are also called "Infinite" Discontinuities

Multiple Choice

• Continuous

• Discontinuous

Multiple Choice

• Continuous

• Discontinuous

Multiple Choice

• Continuous

• Discontinuous

Multiple Choice

• Continuous

• Discontinuous

Multiple Choice

• Continuous

• Discontinuous

Multiple Choice

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

• 3

• -3

• 6

• -6

Multiple Choice

At what value of x will f(x) have a removable discontinuity (hole)?

• x=2

• x=-7

• x=-5

• x=5

Multiple Choice

At what value of x will f(x) have an infinite discontinuity (vertical asymptote)?

• x=2

• x=-7

• x=-5

• x=5

Multiple Choice

Which of the following best describes the continuity at x = 2?

• Jump Discontinuity

• Removable Discontinuity

• Continuous

• Infinite Discontinuity

​Hole at x=-2

Vertical Asymptote at x=5

Multiple Select

Discuss the continuity of the function.

Check all that apply.

• $$\lim_{x\rightarrow1}f\left(x\right)=1$$

• f(1) = 1

• The function is continuous.

• The function is discontinuous at 1 because the limit does not exist.

Multiple Select

Discuss the continuity of the function.

(More than one answer is possible)

• Continuous

• Discontinuous at

  x = 2, nonremovable

• The limit exists at x = 2

• The discontinuity is removable.

Multiple Select

Discuss the continuity of the function.

Check all that apply.

• $$\lim_{x\rightarrow-1}f\left(x\right)=-1$$

• f(-1) = -1

• The function is continuous.

• The function is discontinuous at -1 because the limit does not exist.

Multiple Select

Discuss the continuity of the function.

Check all that apply.

• $$\lim_{x\rightarrow0}f\left(x\right)=1$$

• f(0) = -1

• The function is continuous.

• The function is discontinuous at 0 because the limit does not exist.

Multiple Choice

At which x-value is there a jump discontinuity?

• 3

• 1

• -2

• there is no jump discontinuity

Multiple Choice

At which x-value is there a point discontinuity?

• -2

• 0

• 1

• 3

Multiple Choice

:

• 5

• 1

• -5

• Does not exist

Multiple Choice

What is the $$\lim_{x\rightarrow-5}\ \frac{x^2-25}{x+5}$$  ?

• d.n.e.

• 5

• 10

• -10

Multiple Choice

If $$f\left(x\right)=\frac{8x^3-8}{4x^3-2}$$ , find the value of the following limit.

• 2

• 4

• 8

• +∞

Multiple Choice

What is this limit?

• $$\infty$$

• $$-\infty$$

• 0

• -2/3

• DNE

Multiple Choice

What is the limit of the function as x approaches -4 from the left?

• 2
• -4
• DNE
• -2

Multiple Choice

What is the limit of the function as x approaches 1 from the right?

• DNE
• 1
• 4
• -2

Multiple Choice

Which Graph shows Continuity?

• Graph 1

• Graph 2

Multiple Select

What are the three types of discontinuities (shown in the image?

• Hole (removable)

• Vertical Asymptote (non removable)

• Jump Discontinuity ( non removable)

• transitive discontinuity (removable)

• reflective discontinuity

Multiple Choice

When does a hole or vertical asymptote happen?

• When the function equals zero.

• When the denominator of the function equals zero.

• When the numerator equals zero.

Identify where the discontinuities happen?

Multiple Choice

What can be my first step to find the discontinuities of the function?

• Factor the numerator and denominator

• Cancel the x²

• Plug in zero

Multiple Select

When does the denominator of the factored function equal zero? (select all that apply)

• x= -5

• x= 2

• x= 5

• x= -2

• x= 6

Multiple Select

Identify the Discontinuities

• Vertical Asymptote at x=1

• Hole at x=-1

• Vertical Asymptote at x=-1

• Hole at x=1