Free Printable Basic Cal Q3 Pre-Test 3

1.

Find where the function $f\left(x\right)=-x^3+x^2-1$ is continuous.

a)

$\left(-\infty,-1\right)\left(-1,3\right)\left(3,\infty\right)$

b)

$\left(-\infty,-2\right)\left(-2,3\right)\left(3,\infty\right)$

c)

$\left(-\infty,-3\right)\left(-3,1\right)\left(1,\infty\right)$

d)

$\left(-\infty,\infty\right)$

2.

Which of the following points will make $f\left(x\right)=\sqrt[]{x-1}$ a continuous function?

a)

$x=-1$

b)

$-\frac{1}{2}$

c)

$x=0$

d)

$1$

3.

Which of the following statements about the function given is not true?

a)

$f\left(1\right)$ does not exist

b)

$\lim_{x\rightarrow0^+}f\left(x\right)$ exist

c)

$\lim_{x\rightarrow2^-}f\left(x\right)$ exist

d)

$\lim_{x\rightarrow1}f\left(x\right)$ exist

4.

Find the intervals on which the function shown is continuous.

a)

$\left(-\infty,2\right)\left(2,\infty\right)$

b)

$\left(-\infty,2\right)\left[4,\infty\right)$

c)

$\left(-\infty,2\right]\left(2,\infty\right)$

d)

$\left(-\infty,2\right)\left[2,\infty\right]$

5.

Find the intervals on which the function is continuous; $f\left(x\right)=\frac{x^2+3x-4}{x+4}$

a)

$\left(-\infty,4\right)\left(4,\infty\right)$

b)

$\left(-\infty,4\right)\left[4,\infty\right)$

c)

$\left(-\infty,-4\right)\left(-4,\infty\right)$

d)

$\left(-\infty,-4\right)\left[-4,\infty\right)$

6.

Find the value of c that will make the function continuous.

a)

$-3$

b)

$6$

c)

$12$

d)

$15$

7.

Find the value of a that will make the function continuous.

a)

$1$

b)

$-1$

c)

$2$

d)

$-2$

8.

From the given function, what is the value of $f\left(0\right)$ ?

a)

$1$

b)

$-1$

c)

$-3$

d)

$3$

9.

From the given function, what is the value of $\lim_{x\rightarrow0^-}f\left(x^2-1\right)$ ?

a)

$0$

b)

$-1$

c)

$1$

d)

$-3$

10.

From the given function, what is the value of $\lim_{x\rightarrow0^+}f\left(2x-3\right)$ ?

a)

$0$

b)

$-1$

c)

$1$

d)

$-3$

11.

ON which of the following intervals over which the function $f\left(x\right)=\sqrt[]{x+3}$ is continuous?

a)

$\left[-3,+\infty\right)$

b)

$\left(-3,+\infty\right)$

c)

$\left(-3,3\right)$

d)

$\left[-2,+\infty\right]$

12.

Based on the given graph; determine where the function is continuous.

a)

$x=-8$

b)

$x=-2$

c)

$x=6$

d)

$x=10$

13.

Which of the following statements about the function given is NOT true?

a)

$f\left(2\right)$ does not exist

b)

$\lim_{x\rightarrow2^+}f\left(x\right)$ exist

c)

$\lim_{x\rightarrow2^-}f\left(x\right)$ exist

d)

$\lim_{x\rightarrow2^+}f\left(x\right)=f\left(2\right)$

14.

Where is the function $f\left(x\right)\ =\ \frac{1}{x^2-16}$ discontinuous?

a)

$x=8$

b)

$x=6$

c)

$x=4$

d)

$x=2$

15.

Where is the function $f\left(x\right)\ =\ \frac{2x}{x^2+4x+3}$ discontinuous?

a)

$x=2$

b)

$x=-2$

c)

$x=3$

d)

$x=-3$

Basic Cal Q3 Pre-Test 3

Total questions: 15

Worksheet time: 3hrs 30mins

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