Free Printable Continuity at a Point Quiz

1.

Select the THREE conditions for Continuity at a Point $x=c$ .

a)

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

b)

$f\left(c\right)$ must be positive

c)

$f\left(c\right)$ is defined

d)

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

e)

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

2.

Use the graph shown to determine if the function is continuous at $x=13$ . If the function is not continuous, select the condition for continuity at a point that the function fails.

a)

The function is continuous at $x=13$ .

b)

The function is not continuous at $x=13$ because $f\left(13\right)$ is undefined.

c)

The function is not continuous at $x=13$ because $\lim_{x\rightarrow13}f\left(x\right)$ does not exist.

d)

The function is not continuous at $x=13$ because $\lim_{x\rightarrow13}f\left(x\right)\ne f\left(13\right)$ .

3.

Use the graph shown to determine if the function is continuous at $x=5$ . If the function is not continuous, select the condition(s) for continuity at a point that the function fails.

SELECT ALL THAT APPLY, THERE ARE TWO ANSWERS.

a)

The function is continuous at $x=5$ .

b)

The function is not continuous at $x=5$ because $f\left(5\right)$ is undefined.

c)

The function is not continuous at $x=5$ because $\lim_{x\rightarrow5}f\left(x\right)$ does not exist.

d)

The function is not continuous at $x=5$ because $\lim_{x\rightarrow5}f\left(x\right)\ne f\left(5\right)$ .

4.

Use the graph shown to determine if the function is continuous at $x=18$ . If the function is not continuous, state the type of discontinuity the function has at that point.

a)

The function is continuous at $x=18$ .

b)

The function has a jump discontinuity at $x=18$ .

c)

The function has a removable discontinuity (hole) at $x=18$ .

d)

The function has a non-removable (infinite) discontinuity at $x=18$ .

5.

Use the graph shown to determine if the function is continuous at $x=1$ . If the function is not continuous, state the type of discontinuity the function has at that point.

a)

The function is continuous at $x=1$ .

b)

The function has a jump discontinuity at $x=1$ .

c)

The function has a removable discontinuity (hole) at $x=1$ .

d)

The function has a non-removable (infinite) discontinuity at $x=1$ .

6.

Use the graph shown to determine if the function is continuous at $x=-7$ . If the function is not continuous, state the type of discontinuity the function has at that point.

a)

The function is continuous at $x=-7$ .

b)

The function has a jump discontinuity at $x=-7$ .

c)

The function has a removable discontinuity (hole) at $x=-7$ .

d)

The function has a non-removable (infinite) discontinuity at $x=-7$ .

7.

Use the graph shown to determine if the function is continuous at $x=5$ . If the function is not continuous, state the type of discontinuity the function has at that point.

a)

The function is continuous at $x=5$ .

b)

The function has a jump discontinuity at $x=5$ .

c)

The function has a removable discontinuity (hole) at $x=5$ .

d)

The function has a non-removable (infinite) discontinuity at $x=5$ .

8.

Determine if the function shown is continuous at $x=0$ .

Hint: You will have to use the Unit Circle to evaluate

\cos\ x

.

a)

The function is continuous at $x=0$

b)

The function is not continuous at $x=0$

9.

Determine if the function shown is continuous at $x=3$ .

a)

The function is continuous at $x=3$

b)

The function is not continuous at $x=3$

10.

Evalaute $\lim_{x\rightarrow3}\ \left(\frac{x^2-9}{x^2+5x-24}\right)$

a)

$DNE$

b)

$\frac{6}{11}$

c)

$0$

d)

$\infty$

Continuity at a Point Quiz

Total questions: 10

Worksheet time: 6mins

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