Free Printable Exponential function

1.

Which of the following corresponds to an exponential function?

a)

$f\left(x\right)=ax^2$

b)

$f\left(x\right)=a^x$

c)

$f\left(x\right)=x^a$

d)

$f\left(x\right)\ =\ ax^3$

2.

What type of shift does the following exponential presents?

a)

Horizontal

b)

Vertical

c)

Both

d)

Neither

3.

What type of shift is the following exponential function presenting?

a)

There is no shift present

b)

Vertical shift

c)

Horizontal shift

d)

Both horizontal and vertical shifts

4.

f\left(x\right)=3^x+2

Is an exponential function with ____________________ shift...

a)

Oblique

b)

Horizontal

c)

Vertical

d)

None of the options

5.

Select the graph for $g\left(x\right)=3^{x-1}$

a)

b)

c)

d)

None of the options

6.

The range for the function $f\left(x\right)=4^x-1$ is:

a)

(-1, ∞)

b)

(-∞,∞)

c)

[-1,∞)

d)

(-1,∞]

e)

[-1,∞]

7.

Exponential functions ALWAYS have a vertical asymptote

a)

True

b)

False

8.

For the function y =4^x, what is the ordinate to the origin?

a)

0

b)

1

c)

4

d)

$\not\ni$

9.

The equations that corresponds to this graph, is:

a)

$f(x)=5^x$

b)

$f(x)=5^{x+1}$

c)

$f(x)=5^x-1$

d)

$f(x)=5^{x-1}$

10.

The equations that corresponds to this graph, is:

a)

$f(x)=\left(\frac{4}{5}\right)^x$

b)

$f(x)=\left(\frac{4}{5}\right)^{x-1}$

c)

$f(x)=\left(\frac{4}{5}\right)^{x+1}$

d)

$f(x)=\left(\frac{4}{5}\right)^x+1$

11.

The equations that corresponds to this graph, is:

a)

$f(x)=\left(\frac{5}{9}\right)^{x-8}$

b)

$f(x)=\left(\frac{5}{9}\right)^{x+8}$

c)

$f(x)=\left(\frac{5}{9}\right)^x+8$

d)

$f(x)=\left(\frac{5}{9}\right)^{ }-8x$

12.

An exponential functions has the form $f\left(x\right)=a^x$ , given that:

a)

$0<a>1$ and $a=1$

b)

$a>0$ and $a\ne1$

c)

$a<0$ and $a=1$

d)

$0>a<1$ and $a\ne1$

13.

For exponential functions we can observe that:

a)

$Domain\ f\left(x\right)=\left\{x\left|x\ \epsilon\ R\right|\right\}$

b)

Exponential function intersect the x-axis.

c)

$Range\ f\left(x\right)=\left\{y\left|y\ \epsilon\ R\right|\right\}$

d)

Exponential function do not have ordinate to the origin

14.

An unicelular organism multiplies itself in the following way: Every initial cell divides itself into 3 every 30 minutes.

Which is the algebraic expression that links the 30 minutes period that pass "x" with the amount of cells present "y"?

a)

y=30^x

b)

y=2*3^x

c)

y=3^x

d)

y= 3*3^x

15.

Select the expression(s) that represent an exponential function(s):

a)

y= 2x²

b)

y= 5^x + 2

c)

y=x² - 1

d)

y= 2^x

16.

Which of the following could represent the given graph? (More than one may apply)

a)

F(x)= 32^x

b)

C(x)= 32^-x

c)

D(x)= (1/32)^x

d)

S(x)= (1/32)^-x

17.

Which of the graphs represent the function $f\left(x\right)=3^x$ ?

a)

b)

c)

d)

18.

Which of the graphs represent the function $f\left(x\right)=4^x$ ?

a)

b)

c)

d)

19.

Which of the graphs represent the function $f\left(x\right)=-2^x$ ?

a)

b)

c)

d)

20.

Which of the graphs represent the function $f\left(x\right)=-\left(\frac{1}{2}\right)^x$ ?

a)

b)

c)

d)

21.

Which of the graphs represent the function $f\left(x\right)=7^x$ ?

a)

b)

c)

d)

22.

Which of the graphs represent the function $f\left(x\right)=-\left(\frac{1}{3}\right)^x$ ?

a)

b)

c)

d)

23.

Which of the graphs represent the function $f\left(x\right)=\left(\frac{1}{9}\right)^x$ ?

a)

b)

c)

d)

24.

Which of the graphs represent the function $f\left(x\right)=6^x$ ?

a)

b)

c)

d)

25.

Exponential functions ALWAYS have a horizontal asymptote

a)

True

b)

False

26.

$\log1=0$

a)

TRUE

b)

FALSE

27.

log 10 = ?

a)

0

b)

1

c)

10

d)

undefined

28.

Which of the following expressions corresponds to the exponential form of:
b^e= a ?

a)

log_e a = b

b)

log_a b = e

c)

log_b a = e

d)

log_b e = a

29.

Change the following logarithmic expression to it's exponential form:
log₃ 47 = x

a)

47³ = x

b)

47^x= 3

c)

x³ = 47

d)

3^x = 47

30.

Which of the following are logarithmic functions? (You may select more than one, if applicable)

a)

$f\left(x\right)=2^x+1$

b)

$f\left(x\right)=\left(\frac{1}{3}\right)^4$

c)

$f\left(x\right)=\log_28$

d)

$f\left(x\right)=\log_5\left(x+1\right)$

31.

$\log_28\ =\ ?$

a)

3

b)

8

c)

2

d)

4

32.

$\log_2\frac{1}{2}=?$

a)

-1

b)

0

c)

2

d)

-2

33.

$\ln\sqrt{e^3}=?$

a)

$\frac{3}{2}$

b)

-3

c)

3

d)

$\frac{2}{3}$

34.

$\ln\frac{1}{e^4}=?$

a)

-4

b)

4

c)

$\frac{1}{4}$

d)

0,4

35.

$\log_525\ +\log\ 10=?$

a)

$3$

b)

$2$

c)

$1$

d)

$0$

36.

Which of the following represents the PRODUCT property of logarithms?

a)

$\log_52+\log_63=\log_5\left(2\cdot3\right)$

b)

$\log_52+\log_53=\log_5\left(2\cdot3\right)$

c)

$\log_52+\log_53=\log_52\cdot\log_53$

d)

None of the options

37.

Which of the following represents the QUOTIENT property of logarithms?

a)

$\log_e2-\log_e3=Ln\left(\frac{2}{3}\right)$

b)

$\log_{ }2-\log_13=\log_{ }\left(\frac{2}{3}\right)$

c)

$\log_52-\log_53=\frac{\log_52}{\log_53}$

d)

None of the options

38.

$\log_39+3\log_2\sqrt[3]{2}+4\log_71$ Applying the properties of logarithms simplify completely the expression.

a)

0

b)

1

c)

2

d)

3

e)

None of the options

39.

Rewrite the logarithm into its exponential form:

a)

b)

c)

d)

None of the options

40.

a)

b)

c)

d)

41.

$\log\ \sqrt{\frac{4x}{5}}$ Using the properties of logarithms rewrite the expression into individual logarithms:

a)

$\frac{1}{2}\left(\left(\log\ 4\ +\ \log\ x\right)-\log\ 5\right)$

b)

2 (log 4x -log 5)

c)

$\frac{1}{2\ }\left(\log\ \left(4\div5\right)\ +\log\ x\right)$

d)

None of the options

42.

$\frac{1}{81}=3^{-4}$ , is the same as:

a)

$\log_3\left(\frac{1}{81}\right)=-4$

b)

$\log_4\left(\frac{1}{81}\right)=-3$

c)

$\log_3\left(\frac{1}{81}\right)=4$

d)

$\log_{-3}\left(81\right)=4$

43.

$\log_b\left(\frac{2h}{6p}\right)$ Using the properties of logarithms expand the expression until you get individual logarithms.

a)

Ninguno

b)

$\log_b2\ +\log_bh\ -\log_b6\ -\log_bp$

c)

$\log_b2\ +\log_bh\ +\log_b6\ +\log_bp$

d)

$\log_b2\ +\log_bh\ +\log_b2\ +\log_bh$

44.

$\log_z4\ -\log_z\ p+\log_z\ e$ Using the properties of logarithms, contract the expression into a single logarithm.

a)

$\log_x\left(\frac{4e}{p}\right)$

b)

$\log_x\left(\frac{4r}{2p}\right)$

c)

Ninguno

d)

$\log_x\left(\frac{4e}{o}\right)$

45.

$\log_x\left(4map\right)$ Using the properties of logarithms expand the expression until you get individual logarithms.

a)

$\log_xy\ +\log_x5$

b)

$\log_x4\ +\log_xm+\log_xa+\log_xp$

c)

$\log_x4+\ \log_x10+\log_x8$

d)

None of the options

46.

$\log_2\left(\frac{4}{m}\right)\ =\frac{\log_2\left(4\right)}{m}$

a)

TRUE

b)

FALSE

47.

Which of the following is and equivalent expression to $\log_w\left(p\cdot t\right)$ ?

a)

$\log_wp+\log_wt$

b)

$\log_wp\cdot\log_wt$

c)

$\log_wp-\log_wt$

d)

$\frac{\log_wp}{\log_wt}$

Exponential function

Total questions: 47

Worksheet time: 22mins

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