Free Printable NTI Exam

1.

What does an inverse function do?

a)

Nothing

b)

Makes it bigger

c)

Does the opposite of the original function

2.

What is the equation that the inverse will reflect across?

a)

y = x

b)

y = 0

c)

x = 0

d)

Potato

3.

Find the inverse of f(x) = -4x - 12

a)

f^-1(x) = 4x - 3

b)

f^-1(x) = -1/4x - 3

c)

f^-1(x) = 1/4x + 3

d)

f^-1(x) = -4x - 3

4.

Find the inverse function

a)

b)

c)

d)

5.

Find the inverse of f(x) = x² - 5

a)

f^-1(x) = ±√(x) + 5

b)

f^-1(x) = ∛(x-5)

c)

f^-1(x) = ±√(x+5)

d)

f^-1(x) = x² - 5

6.

Find the inverse function

a)

b)

c)

d)

7.

Are the following inverses of each other?

a)

Yes

b)

No

8.

Which is the inverse of the table?

a)

b)

c)

d)

9.

Here is the domain and range for a function:

D: (-∞, ∞)

R: [3, ∞)

What is the domain and range of the inverse?

a)

D: [3, ∞)

R: (-∞, ∞)

b)

D: (-∞, ∞)

R: [3, ∞)

10.

Create a table for $f\left(x\right)=\left(x-1\right)^2+2$ and its inverse and choose the correct graph for both.

a)

b)

c)

11.

Create a table for $f\left(x\right)=-4x+12$ and its inverse and choose the graph of both.

a)

b)

c)

12.

Is this exponential growth or decay and why?

a)

Growth bc a>1.

b)

Decay bc b>1

c)

Decay bc 0<b<1

d)

Growth bc 0<b<1

13.

A population of fish starts at 8,000 and decreases by 6% per year. Write an equation to model this situation.

a)

$f\left(x\right)=8000\left(6\right)^x$

b)

$f\left(x\right)=8000\left(.94\right)^x$

c)

$f\left(x\right)=8000\left(.06\right)^x$

d)

$f\left(x\right)=6\left(8000\right)^x$

e)

$f\left(x\right)=8000\left(1.06\right)^x$

14.

A population of fish starts at 8,000 and decreases by 6% per year. What is the population of fish after 10 years?

a)

14327

b)

4309

c)

839

d)

7680

15.

Twenty years ago, Mr. Davis purchased his home for $160,000. Since then, the value of the home has increased about 5% per year. How much is the home worth today?

a)

$176,783.29

b)

$424,527.63

c)

$57,357.75

d)

$532,041,076.80

16.

The special number, natural base "e", is a ________________ number.

a)

rational

b)

irrational

c)

real

17.

Simply the expression. $e^{-2}\cdot e^8$

a)

$e^{-16}$

b)

$\frac{1}{e^2e^8}$

c)

$e^6$

d)

$e^{-10}$

18.

Simplify: $\left(3e^{-5x}\right)^4$

a)

$\frac{3}{e^{20x}}$

b)

$\frac{1}{81e^{20x}}$

c)

$81e^{20x}$

d)

$\frac{81}{e^{20x}}$

19.

Simplify the expression. $\frac{-7e^2}{49e^{17}}$

a)

$\frac{-7}{e^{15}}$

b)

$\frac{-1}{7e^{15}}$

c)

$\frac{e^{-15}}{7}$

d)

$7e^{15}$

20.

Write in exponential form:
$\log_2256=8$

a)

$2^8=256$

b)

$8^2=256$

c)

$256^8=2$

d)

$256^2=8$

21.

Write in exponential form:
$\log_{\frac{1}{3}}243=-5$

a)

$\left(\frac{1}{3}\right)^{-5}=243$

b)

$243^{\frac{1}{2}}=-5$

c)

$\left(\frac{1}{3}\right)^{243}=-5$

d)

$\left(3\right)^{-5}=243$

22.

Write in logarithmic form:
$6^{-2}=\frac{1}{36}$

a)

$\log_{-2}6=\frac{1}{36}$

b)

$\log_{ }6=\frac{1}{36}$

c)

$\log_{\frac{1}{36}}6=-2$

d)

$\log_6\left(\frac{1}{36}\right)=-2$

23.

Write in logarithmic form:
$10^3=1000$

a)

$\log_{10}\left(3\right)=1000$

b)

$\log\left(1000\right)=3$

c)

$\log_{1000}\left(3\right)=10$

d)

$\ln\left(1000\right)=3$

24.

Find the inverse: $y=4\left(3\right)^{x-5}$

a)

$y^{-1}=\log_3\left(\frac{x}{4}\right)+5$

b)

$y^{-1}=\log_3\left(\frac{x}{4}\right)-5$

c)

$y^{-1}=\log_3\left(x\right)+5$

d)

$y^{-1}=\log_3\left(x\right)-5$

25.

Find the inverse of the function $f\left(x\right)=2^{x+1}-5$

a)

$\log_2\left(x-1\right)-5$

b)

$\log_2\left(x-5\right)-1$

c)

$\log_2\left(x+5\right)-1$

d)

$\log_2\left(x+4\right)$

26.

Find the inverse of $f\left(x\right)=\log_2\left(x+3\right)$

a)

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

b)

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

c)

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

d)

$f^{-1}\left(x\right)=2^{x+3}$

27.

Find the inverse: $y=\log_{ }\left(x-2\right)+5$

a)

$y=\log\left(x-2\right)+5$

b)

$y=10^x+3$

c)

$y=10^{x-5}+2$

d)

$y=10^{x-5}-2$

28.

The population of Madison, Indiana, can be modeled by P=4322(1.02)^twhere t is the number of years since 1987. What was the population in 1987?

a)

2 people

b)

It doesn't say

c)

1.02

d)

4322

29.

You drink a beverage with 95 mg of caffeine. Each hour, the caffeine in your system decreases by about 6%. How long until you have 10mg of caffeine?

a)

36 hours exactly

b)

36 to 37 hours

c)

35 to 36 hours

d)

37 hours exactly

30.

$4^{\left(x-2\right)}=15$ Solve for x.

a)

3.9534

b)

-.04655

c)

2.0437

d)

1.8502

31.

$2+e^{\left(x+4\right)}=1$ Solve for x.

a)

-2.9014

b)

1.9459

c)

No Solution bc you can't take the log of $e$ .

d)

No Solution bc you can't take the natural log of a negative number.

32.

Solve for x. $6^{\left(3x+5\right)}=6^{\left(-4x\right)}$

a)

-7/5

b)

-5/7

c)

5/7

d)

5

e)

-5

33.

Solve for k: $2^{\left(k+4\right)}=\frac{1}{16}$

a)

0

b)

8

c)

-8

d)

2

34.

Solve for x. $125^{\left(-2x\right)}=15625^2$

a)

1/2

b)

-1/2

c)

-2

d)

2

35.

$y=\ 6^x$ Find the inverse of

a)

$y^{-1}=\log_x6$

b)

$y^{-1}=\log_6x$

c)

$y^{-1}=\log_y6$

d)

$y=\log_{ }6$

NTI Exam

Total questions: 35

Worksheet time: 8hrs 33mins

Similar Resources on Wayground