Free Printable Quiz Review 2.1

1.

Match each exponential function with its end behavior written in limit notation

a)

$5^x$

1.

$\lim_{x\rightarrow-\infty}f\left(x\right)=0\ and\ \lim_{x\rightarrow\infty}f\left(x\right)=\infty$

b)

$-2\left(\frac{4}{3}\right)^x$

2.

$\lim_{x\rightarrow-\infty}f\left(x\right)=0\ and\ \lim_{x\rightarrow\infty}f\left(x\right)=-\infty$

c)

$5\left(\frac{3}{8}\right)^x$

3.

$\lim_{x\rightarrow-\infty}f\left(x\right)=\infty\ and\ \lim_{x\rightarrow\infty}f\left(x\right)=0$

d)

$-6\left(0.2\right)^x$

4.

$\lim_{x\rightarrow-\infty}f\left(x\right)=-\infty\ and\ \lim_{x\rightarrow\infty}f\left(x\right)=0$

2.

Let $g$ be an exponential function that is increasing and concave down. Which of the following could be the graph of $g$ ?

a)

b)

c)

d)

3.

The graph of the exponential function h is shown. Which of the following could be the expression for h?

a)

$h\left(x\right)=-2\left(\frac{2}{3}\right)^x$

b)

$h\left(x\right)=-\frac{2}{3}\left(2\right)^x$

c)

$h\left(x\right)=\frac{2}{3}\left(2\right)^x$

d)

$h\left(x\right)=2\left(\frac{2}{3}\right)^x$

4.

Let $g\left(x\right)=-2\left(5\right)^x$ . Which of the following statements about the graph of f is correct?

a)

g is increasing at an increasing rate

b)

g is increasing at an decreasing rate

c)

g is decreasing at an increasing rate

d)

g is decreasing at an decreasing rate

5.

Let $f\left(x\right)=3^x$ . Which of the following statements about the graph of f is correct?

a)

f is increasing at an increasing rate

b)

f is increasing at an decreasing rate

c)

f is decreasing at an increasing rate

d)

f is decreasing at an decreasing rate

6.

The exponential function k exhibits exponential decay. Which of the following could be k?

a)

$k\left(x\right)\ =\ 4\left(\frac{2}{3}\right)^x$

b)

$k\left(x\right)\ =\ \frac{2}{3}\left(4\right)^x$

c)

$k\left(x\right)\ =\ -4x^2$

d)

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

7.

The graph of the exponential function g has the following end behaviors:

$\lim_{x\rightarrow-\infty}g\left(x\right)=0\ and\ \ \lim_{x\rightarrow\infty}g\left(x\right)=-\infty$

Which of the following could be an equation for g?

a)

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

b)

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

c)

$g\left(x\right)=3\left(\frac{1}{2}\right)^x$

d)

$g\left(x\right)=\frac{1}{2}\left(3\right)^x$

8.

Let h be an exponential function defined by $h\left(x\right)=5\left(\frac{\pi}{3}\right)^x$ . Which of the following statements is correct?

a)

h is increasing and the graph of h is concave up

b)

h is increasing and the graph of h is concave down

c)

h is decreasing and the graph of h is concave up

d)

h is decreasing and the graph of h is concave down

9.

Match the graphs of the exponential functions below with the corresponding description of the graph

a)

1.

The graph is decreasing and concave down

b)

2.

The graph is decreasing and concave up

c)

3.

The graph is increasing and concave down

d)

4.

The graph is increasing and concave up

10.

Match the graphs of the exponential functions below with the corresponding description of the graph

a)

1.

Decreasing at a decreasing rate

b)

2.

Decreasing at an increasing rate

c)

3.

Increasing at a decreasing rate

d)

4.

Increasing at a increasing rate

11.

Let $f\left(x\right)=3^x$ . Let $g\left(x\right)$ be a transformation of $f$ . If $g\left(x\right)=\frac{f\left(x\right)}{27}$ , name the transformation of $f$

a)

Shifts left 3 units

b)

Shifts right 3 units

c)

Horizontal dilation of 3

d)

Horizontal dilation of 1/3

12.

Let $f\left(x\right)=8^x$ . Let $g\left(x\right)$ be a transformation of $f$ . If $g\left(x\right)=\frac{f\left(x\right)}{8}$ , name the transformation of $f$

a)

Horizontal dilation by 1/2

b)

Horizontal dilation by 2

c)

Shift left 1

d)

Shift right 1

13.

Let $f\left(x\right)=5^x$ . Let $g\left(x\right)$ be a transformation of $f$ . If $g\left(x\right)=125^x$ , name the transformation of $f$

a)

Horizontal dilation of 1/3

b)

Horizontal dilation of 3

c)

Shift right 3

d)

Shift left 3

14.

Let $f\left(x\right)=9^x$ . Let $g\left(x\right)$ be a transformation of $f$ . If $g\left(x\right)=81^x$ , name the transformation of $f$

a)

Shift right 2

b)

Shift left 2

c)

Horizontal dilation by 1/2

d)

Horizontal dilation by 2

15.

Determine if the sequence is Arithmetic, Geometric, or Neither

1/2, 13/6, 23/6, 11/2, 43/6, .....

a)

Geometric

b)

Neither

c)

Arithmetic

16.

Determine if the sequence is Arithmetic, Geometric, or Neither

-3, -15, -75, -375, .....

a)

Geometric

b)

Neither

c)

Arithmetic

17.

Determine if the sequence is Arithmetic, Geometric, or Neither

-9, -7, -4, 0, 5, .....

a)

Geometric

b)

Neither

c)

Arithmetic

18.

Let $a_n$ be an arithmetic sequence where $a_{12}=117\ and\ a_{32}=297$ . What is the common difference?

19.

Let $a_n$ be an arithmetic sequence where $a_{12}=117\ and\ a_{32}=297$ . Find $a_{35}$

20.

Let $a_n$ be an arithmetic sequence where $a_{17}=-115\ and\ a_{37}=-235$ . What is the common difference?

21.

Let $a_n$ be an arithmetic sequence where $a_{17}=-115\ and\ a_{37}=-235$ . Find $a_{35}$

22.

Let $g_n$ be a geometric sequence with $g_3=-72\ and\ g_6=15552$ . What is the common ratio?

23.

Let $g_n$ be a geometric sequence with $g_3=-72\ and\ g_6=15552$ . Find $g_8$

24.

Let $g_n$ be a geometric sequence with $g_3=100\ and\ g_5=2500$ . What is the common ratio?

25.

Let $g_n$ be a geometric sequence with $g_3=100\ and\ g_5=2500$ . Find $g_8$

26.

Determine if the function given in the table is linear or exponential and justify.

a)

Linear because as the input values increase by 10, the outputs change by a constant of 1/2

b)

Linear because as the input values increase by 10, the outputs change proportionally by a ratio of 1/2

c)

Exponential because as the input values increase by 10, the outputs change proportionally by a ratio of 1/2

d)

Exponential because as the input values increase by 10, the outputs change by a constant of 1/2

27.

Determine if the function given in the table is linear or exponential and justify.

a)

Linear because as the input values increase by 3, the outputs change by a constant of -2.5

b)

Linear because as the input values increase by 3, the outputs change proportionally by a ratio of -2.5

c)

Exponential because as the input values increase by 3, the outputs change proportionally by a ratio of -2.5

d)

Exponential because as the input values increase by 3, the outputs change by a constant of -2.5

28.

Determine if the function given in the table is linear or exponential and justify.

a)

Linear because as the input values increase by 5, the outputs change by a constant of 3

b)

Linear because as the input values increase by 5, the outputs change proportionally by a ratio of 3

c)

Exponential because as the input values increase by 5, the outputs change proportionally by a ratio of 3

d)

Exponential because as the input values increase by 5, the outputs change by a constant of 3

29.

Determine if the function given in the table is linear or exponential and justify.

a)

Linear because as the input values increase by 4, the outputs change by a constant of -3

b)

Linear because as the input values increase by 4, the outputs change proportionally by a ratio of -3

c)

Exponential because as the input values increase by 4, the outputs change proportionally by a ratio of -3

d)

Exponential because as the input values increase by 4, the outputs change by a constant of -3

Quiz Review 2.1 - 2.4

Total questions: 29

Worksheet time: 41mins

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