Free Printable IVT and Continuity

1.

Given $f\left(x\right)=-6x^2+2$ on [-2, 1].

Which of these y-coordinates are guaranteed by the IVT?

Select all the apply.

a)

5

b)

0

c)

-3

d)

-6

e)

None. The function is not continuous on that interval.

2.

Given $f\left(x\right)=\frac{x}{x+3}$ on [-2, 1].

Which of these y-coordinates are guaranteed by the IVT?

Select all the apply.

a)

5

b)

0

c)

-1

d)

-6

e)

None. The function is not continuous on that interval.

3.

Given $f\left(x\right)=\frac{x+6}{x-2}$ on [0, 3].

Which of these y-coordinates are guaranteed by the IVT?

Select all the apply.

a)

5

b)

0

c)

-1

d)

-6

e)

None. The function is not continuous on that interval.

4.

Given $f\left(x\right)=x^3-x^2+2$ on [-1, 1].

Which of these y-coordinates are guaranteed by the IVT?

Select all the apply.

a)

1

b)

-1

c)

$-\frac{1}{2}$

d)

$\frac{1}{2}$

e)

None. The function is not continuous on that interval.

5.

Given $f\left(x\right)=\sqrt[]{5-x}$ on [-20, 1].

Which of these y-coordinates are guaranteed by the IVT?

Select all the apply.

a)

6

b)

0

c)

3

d)

-5

e)

None. The function is not continuous on that interval.

6.

What value of A will make f(x) a continuous function at x=1?

(a)

7.

Is f continuous at x=-2?

If not, which stage of continuity does f fail first?

a)

i.

f(c) is defined

b)

ii.

$\lim_{x\rightarrow c}f\left(c\right)$ exists

c)

iii. $\lim_{x\rightarrow c}f\left(x\right)=f\left(c\right)$

d)

f is continuous at x=c

8.

f(x) is discontinuous at x=-2.

What type of discontinuity?

a)

removable

b)

jump

c)

infinite

9.

Find the value of c that makes f(x) continuous at x=-1.

(a)

10.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

11.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

12.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

13.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

14.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

15.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

16.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

17.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

18.

Name the discontinuity at x=2.

a)

Infinite Discontinuity

b)

Removable Discontinuity

c)

Jump Discontinuity

d)

Continuous at x=2

IVT and Continuity

Total questions: 18

Worksheet time: 34mins

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