Free Printable Exponential Functions Transformations

1.

How has the function $7\left(3\right)^x-5$ been transformed from the parent function $7\left(3\right)^x$ ?

a)

Shifted up 5

b)

Shifted down 5

c)

Reflection over the x-axis

d)

Reflection over the y-axis

2.

What is the function of the graph?

a)

$y=-\left(\frac{1}{4}\right)^x-2$

b)

$y=4^x-2$

c)

$y=-4^x-2$

d)

$y=\left(\frac{1}{4}\right)^x-2$

3.

Given the original exponential function defined by y=4^x, how would the graph change if the function were:

y=2(4)^x-3+1?

a)

Interseccion y: 2, right 3, and up 1

b)

Interseccion y: 2, left 3 and down 1

c)

Interseccion y: 4, right 3, and down 1

d)

Interseccion y: 4, left 3, and up 1

4.

Which of the following is an exponential decay? (Check all that apply)

a)

y = 5⋅(1/5)^x

b)

y = 5⋅(7/2)^x

c)

y = 5 (0.8)^x

d)

y = 5(3.5)^x

5.

What is the a-value of the function?

a)

4

b)

3

c)

2

d)

1

6.

Which function represents the table of values?

a)

f(x) = 4x

b)

f(x) = x⁴

c)

f(x) = 4^x

d)

f(x) = 4^x-1

7.

Which of the following functions shows an initial amount of $15 and an increase of 35% each year?

a)

y = 15(35)^x

b)

y = 15(1.35)^x

c)

y = 15(0.35)^x

d)

y = 35(1.15)^x

8.

The number of mosquitoes at the beginning of the summer was 4,000. The population of mosquitoes is expected to grow at a rate of 25% a month. How many mosquitoes will there be after 4 months?

a)

9766

b)

9006

c)

9765

d)

5433

9.

What is the y-intercept of the function?

a)

2

b)

3

c)

1

d)

-2

10.

What is the transformation?

a)

Vertical Translation up 2

b)

Vertical Translation down 2

c)

Horizontal Translation left 2

d)

Horizontal Translation right 2

11.

What is the transformation?

a)

Vertical Translation up 2 and Horizontal translation right 1

b)

Vertical Translation down 2 and Horizontal Translation left 1

c)

Horizontal Translation left 2 and Vertical Translation up 1

d)

Horizontal Translation right 2 and Vertical Translation down 1

12.

Write an equation that models the following situation:

Samantha's hair was known to grow very rapidly. It began at a length of 6 in and grew at a rate of 14% a week.

a)

y=6(0.14)^x

b)

y=6(1+14)^x

c)

y=6(1.14)^x

d)

y=6(0.86)^x

13.

What is the balance of $6000 compounded annually at a rate of 4% for 10 years?

a)

$8,881.47

b)

$7,432.93

c)

$8,400

d)

$6,500

14.

The population of a country is 50 millions of inhabitants. If it grows exponentially in a rate of 2% per year, calculate the estimated population in 15 years

a)

1.02 million people

b)

6 years

c)

3.5 years

d)

67.3 million people

e)

2%

15.

The population of Winnemucca, Nevada, can be modeled by P=6191(1.04)^twhere t is the number of years since 1990. What was the population in 1990?

a)

0 people

b)

104

c)

6,498.64

d)

6191

16.

What is the value of f(-2)? $f\left(x\right)=2\left(3\right)^{x^{ }}-1$
(Substitute and be careful with order of operations)

a)

$19$

b)

$-\frac{7}{9}$

c)

$13$

d)

$\frac{11}{9}$

17.

What is the y-intercept of the function $y=4\left(5\right)^x?$

a)

(0, 0)

b)

(0, 4)

c)

(0, 5)

18.

a)

f(x)=2^x-1-3

b)

f(x)=2^x-1+3

c)

f(x)=2^x+1-3

d)

f(x)=2^x+1+3

19.

The value of a car is $15,000 and depreciates at a rate of 8% per year. What is the decay factor?

a)

^.08

b)

^1.08

c)

.92

d)

8

20.

Classify the model as Exponential GROWTH or DECAY.
A=1200(.85)⁶

a)

Growth

b)

Decay

21.

Compare f(x) = 3^x- 4 with the basic function g(x) = 3^x

a)

4 units up

b)

4 units to the left

c)

4 units to the right

d)

4 units down

22.

Simplify the exponential expression:

a)

10x^-2

b)

2x²

c)

2x¹²

d)

10x¹²

23.

Simplify the exponential expression.

a)

2x⁶y¹²

b)

2x⁵y⁷

c)

8x⁶y¹²

d)

8x⁵y⁷

24.

a)

2a²b⁶

b)

1/2a²b⁶

c)

b⁶/2a²

d)

2b⁶/a²

25.

Utilizando leyes de los exponentes simplifique la expresión tan pequeña como sea posible
$\frac{\left(5x\right)^2\left(5y^3\right)}{\left(5x^3y^4\right)^3}$

a)

$\frac{1}{x^7y^9}$

b)

$\frac{1}{5xy}$

c)

$\frac{1}{x^4y^4}$

d)

$\frac{5}{xy}$

26.

$\frac{25a^{-3}b^{-9}c^4}{5a^2c^{-8}}$

Simplifica y no dejes exponentes negativos

a)

$\frac{5c^{12}}{a^5b^9}$

b)

$\frac{5c^6}{a^5b^9}$

c)

$\frac{5c^{12}}{a^4b^7}$

d)

$\frac{5c^{12}}{a^9b^5}$

27.

$\frac{1}{3\upsilon^{-2}}$

Simplifica y no dejes exponentes negativos

a)

$\frac{v^2}{3}$

b)

$\frac{v^{ }}{3}$

c)

$\frac{v^3}{3}$

d)

$\frac{v^2}{3v}$

28.

$\left(-5\ x^{-7}\ \ y^{4\ }\ \ z^{-2}\ \right)\ \left(\ 2\ x^3\ \ y\ \ z^6\ \right)$ Resuelva el ejercico y seleccione la respuesta correcta.

a)

$\frac{-10\ \ y^5\ \ \ z^4}{x^4}$

b)

$-10\ x^{-4}\ \ y^5\ \ z^4\$

c)

$\frac{-10\ \ \ y^4\ \ z\ ^4\ }{x^4}$

29.

√48

a)

4√2

b)

6√3

c)

4√3

d)

4√2

30.

√96

a)

4√6

b)

3√6

c)

6√5

d)

6√8

31.

√45x⁴y⁷

a)

3x²y³√5

b)

9x²y³√5y

c)

3x²y³√5y

d)

3x⁴y⁷

32.

Simplify the radical expression:
$\sqrt{2x^2y^3}$

a)

$2y\sqrt{xy}$

b)

$2x\sqrt{y^2}$

c)

$y\sqrt{2xy}$

d)

$xy\sqrt{2y}$

33.

Simplify the radical expression:
$\sqrt{128a^3b^4}$

a)

$8ab^2\sqrt{2a}$

b)

$2a\sqrt{8ab^2}$

c)

$2ab\sqrt{64ab}$

d)

$64ab^2\sqrt{2a}$

34.

To solve 8 = 2^5x+7, you would need to re-write 8 as what base?

a)

8

b)

4

c)

2

d)

Cannot be determined

35.

Solve 8 = 2^5x+7

a)

⅘

b)

¼

c)

-⅘

d)

-¼

36.

Solve 3³ = 3^{4x + 2}

a)

¼

b)

-¼

c)

½

d)

-½

37.

Solve for n:
2^-2n = 2⁶

a)

-1

b)

-7

c)

5

d)

-3

38.

Rewrite log₂8 = 3 in exponential form.

a)

2⁸ = 3

b)

2³ = 8

c)

3² = 8

d)

8³ = 2

39.

Write in exponential form

log₂32 = 5

a)

2^-5 = 32

b)

2³² = 5

c)

2⁵ = 32

d)

32⁵ = 2

40.

Write in logarithmic form.
5² = 25

a)

log₅2 = 25

b)

log₂25 = 5

c)

log₂₅5 = 2

d)

log₅25 = 2

Exponential Functions Transformations

Total questions: 40

Worksheet time: 2hrs 0mins

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