Unit 8 test · Web viewUnit 8 testName _____ Algebra1Teachers @ 2015Page 19. Algebra1Teachers @...

Unit 8 test Name ___________________________

Evaluate the expression.

1.

2.

3.

4.

Using a graphing calculator, graph the function f (x)=2x and sketch the graph on the grid provided below.

1. Is the graph an increasing or decreasing function? Explain your answer.

HighSchoolMathTeachers@2020

Unit 8 test Name ___________________________

2. Trace or use the table feature on your calculator to fill out the tables below.As the value of x gets very large, what happens to the value of 2x ?

X 2x

015

1020

As the value of x gets very small, what happens to the value of 2x ?

X 2x

-1-3-5

-10-20

3. Will the value of 2x ever equal 0? Explain your answer.

4. Are there any values of x that would make 2x undefined? Explain your answer

Without graphing, determine whether each function represents exponential growth or exponential decay.

1. y=129 (1.63)x 2. f ( x )=2(0.65)x 3.y=12(17/10)x 4.y=0.8(1/8)x

_____________ ______________ _______________ ______________


Unit 8 test Name ___________________________

The number of bacteria in a culture doubles each hour. Which graph below best represents this situation? Explain your answer.

A. B.

C. D.


Unit 8 test Name ___________________________

1. a. The two equations below represent two different populations of Skeeters. Graph both equations on the same set of axes. When will these populations be approximately the same size?

1. y=10 •1.5x

2. y=1 •2 x

b. Find the size of each population when x=0. What do these values represent?

2. The table below shows the population of Skeeters in a container after each of 5 shakes. Write an equation which could be used to describe this data. (Your equation may not describe the data exactly.)

Shake Number Population Total0 21 72 253 864 3005 1050


Unit 8 test Name ___________________________

Simplify each Radical Expression. If necessary use absolute value signs.1. 3√40h2

2. √63c7b

3. 3√64 s3

4. 3√8


Unit 8 test Name ___________________________

Simplify by combining like terms.

1. 2√5 x+5√5 x−2√5 x

2. 5√3b−2√3b+4 √3b

3. 2√3+√12

4. 5√2+√18

Write each expression in simplest radical form (using at most one radical sign).

1. 8112=¿

2. 27−12 =¿

3. x13 x

13=¿

4. (a−45 )−5

=¿


Unit 8 test Name ___________________________

Simplify completely.

1. 2x√x

2. 2a√3b

3. √4b√2a

4.2 y3√ x


Unit 8 test Name ___________________________

Sketch the graph of each function

1. f ( x )=4∗2x 2. f ( x )=5∗(12 )

x


Unit 8 test Name ___________________________

3. y=4∗2x 4. y=4∗( 12 )

x


Unit 8 test Name ___________________________

Exponential Growth: Investing

1. You deposit $1500 in an account that pays 6% interest compounded yearly. Find the balance after 5 years.

Equation:

Balance after 5 years:

2. You deposit $3500 in an account that pays 8.4% interest compounded yearly. Find the balance after 9 years.

Equation:



Unit 8 test Name ___________________________

3. Which option gives the greater balance? Show the balance for each option.a. Put $500 in an account that pays 7.5% interest compounded yearly for 9

years.

Equation:


b. Put $700 in an account that pays 6.5% interest compounded yearly for 8 years.

Equation:


Which investment is better?


Unit 8 test Name ___________________________

4. Which option gives the greater balance? Show the balance for each option.a. Put $2000 in an account that pays 8% interest compounded yearly for

10 years.

Equation:


b. Put $1500 in an account that pays 12% interest compounded yearly for 8 years.

Equation:


Which investment is better?


Unit 8 test Name ___________________________

1. Write the equation for the function that results from each transformation applied to the base function y=5x .

a) translate down 3 unit b) shift right 2 units

c) translate left ½ unit d) shift up 1 unit and left 2.5 units

2. Describe the transformations that map the function y=8xonto each function.

a) y=( 12 )8x b) y=84 x

c) y=−8x d) y=8−2 x

3. Write the equation for the function that results from each transformation applied to the base function y=7x

a) reflect in the x-axis (vertical reflection) b) stretch vertically by a factor of 3

c) stretch horizontally by a factor of 2.4 d) reflect in the y-axis and stretch vertically by bafo 7

4. Sketch the graph of y=(−12 )2x−4 by using y=2xas the base and applying transformations.


Unit 8 test Name ___________________________

1. Using the two given values fill in the missing numbers for a linear function and for an exponential function.

a 0 1 2 3 4Linear 3 48Exponential 3 48

b 0 1 2 3 4Linear -12 -0.75Exponential -12 -0.75

2. You plan on saving money for college. You start when you are 8 years old with $500 that you earned during the summer. You plan on earning 8% per year on your investment. What is the exponential function that shows how much you will make? Complete the table and graph. How much money will you have after 5 years? 8 years? 10 years?

t f(t)0123


f(t)=

f(5)=

f(8)=

f(10)=

Unit 8 test Name ___________________________

3. Fill in the function table and plot the points, connect the points in order. Show your work!

x f ( x )=6( 13 )

x

f (x) (x , f ( x ))

-101234


Unit 8 test Name ___________________________

Answer KeyEvaluate the expression.

1. 42⋅ 44=42+4=46=40962. ¿¿

3. 52

55 =52⋅5−5=52−5=5−3= 153 =

1125

4. ¿

Using a graphing calculator, graph the function f (x)=2x and sketch the graph on the grid provided below.

5. This is increasing graph. When a>0 and b is greater than 1, the graph will be increasing. In our case, a=1 and b=2.

6. Trace or use the table feature on your calculator to fill out the tables below.As the value of x gets very large, what happens to the value of 2x ?

X 2x

0 11 25 32

10 102420 1048576

As the value of x gets very small, what happens to the value of 2x ?

X 2x

-1 0.5

-3 0.125

-5 0.03125

-10 0.0009765625

-20 0.00000095367431640625


Unit 8 test Name ___________________________

7. As the value of x gets very small, the value of 2x will approach to 0, but it will never be equal to 0.

8. Exponential function y=2x is defined for all real numbers. So, it will never be undefined.

Without graphing, determine whether each function represents exponential growth or exponential decay.

1. y=129 (1.63)x 2. f ( x )=2(0.65)x 3.y=12(17/10)x 4.y=0.8(1/8)x

Growth Decay Growth Decay_____________ ______________ _______________ ______________

The number of bacteria in a culture doubles each hour. Which graph below best represents this situation? Explain your answer.

D. Graph D is the answer. We can write this function as y=2x and that function represents the graph D.

1. a. The two equations below represent two different populations of Skeeters. Graph both equations on the same set of axes. When will these populations be approximately the same size?

1. y=10 •1.5x

2. y=1 •2 x

They will never be the same size.


1

2

Unit 8 test Name ___________________________

b. Find the size of each population whenx=0. What do these values represent?When x=0

y 1=10y 2=0

The values represent the population at start.

2. The table below shows the population of Skeeters in a container after each of 5 shakes. Write an equation which could be used to describe this data. (Your equation may not describe the data exactly.) Answer y=2∙ (3.5 )x

Simplify each Radical Expression. If necessary use absolute value signs.1. 3√40h2=2 3√5h2

2. √63c7b=3√7bc7

3. 3√64 s3=4 s4. 3√8=2

Simplify by combining like terms.

1. 5√5x2. 7√3b3. 4 √34. 8√2

Write each expression in simplest radical form (using at most one radical sign).

1. 9

2. 39

3. 3√ x2

4. a4

Simplify completely.

1. 2√2

2. 2a√3b3b

3. √ 2ba

4. 2 y 3√ x2

x


Unit 8 test Name ___________________________

Sketch the graph of each function

1. f ( x )=4∗2x 2. f ( x )=5∗(12 )

x

3. y=4∗2x 4. y=4∗( 12 )

x


Unit 8 test Name ___________________________

Exponential Growth: Investing

1. Equation: A=1500∙ (1.06 )t

Balance after 5 years: A=$2007.34

2. Equation: A=3500∙ (1.084 )t


3. a. Put $500 in an account that pays 7.5% interest compounded yearly for 9

years.

Equation: A=500∙ (1.075 )t

Balance after 9 years: A=$ 958.62

b. Put $700 in an account that pays 6.5% interest compounded yearly for 8 years.

Equation: A=700∙ (1.065 )t


Second investment (option B) is better.Which option gives the greater balance? Show the balance for each option.

a. Equation: A=2000∙ (1.08 )t

Balance after 10 years: A=$ 4317.85

b. Equation: A=1500∙ (1.12 )t

Balance after 8 years: A=¿3713.94

First Investment (options A) is better


Unit 8 test Name ___________________________

1. Write the equation for the function that results from each transformation applied to the base function y=5x .

a) y=5x−3b) y=5x−2

c) y=5x+ 1

2

d) y=5x+2.5+12. Describe the transformations that map the function y=8xonto each function.

a) Vertically shrinks the graph by 12

b) Horizontally shrinks the graph by 4.

c) Reflects the graph about x-axis

d) Horizontally shrinks the graph by 2 and reflect the graph about y-axis

3. Write the equation for the function that results from each transformation applied to the base

function y=7x

a) y=−(7 )x

b) y=3 ∙ (7 ) x

c) y= (7 )2.4 x

d) y=7 ∙ (7 )−x

4. Sketch the graph of y=(−12 )2x−4 by using y=2xas the base and applying transformations.


Unit 8 test Name ___________________________

1. Using the two given values fill in the missing numbers for a linear function and for an exponential function.

a 0 1 2 3 4Linear 3 14.25 25.5 36.75 48

Exponential 3 6 12 24 48

b 0 1 2 3 4Linear -12 -9.1875 -6.375 -3.5625 -0.75

Exponential -12 -6 -3 -1.5 -0.75

2. f (t )=500 ∙1.08t

t f(t)0 5001 5402 583.23 629.856


f(t)= 500 ∙1.08 t

f(5)= 734.66

f(8)= 925.47

f(10)= 1079.46

Unit 8 test Name ___________________________

3. Fill in the function table and plot the points, connect the points in order. Show your work!

x f ( x )=6( 13 )

x

f (x) (x , f ( x ))

-1 f ( x )=6∙ (13 )

−1 18 (−1 ,18)

0 f ( x )=6∙ (13 )

−0 6 (0 ,6)

1 f ( x )=6∙ (13 )

1 2 (1 ,2)

2 f ( x )=6∙ (13 )

2 2/3 (2 , 23)

3 f ( x )=6∙ (13 )

3 2/9 (3 , 29)

4 f ( x )=6∙ (13 )

4 2/27 (4 , 227

)


Unit 8 test Name ___________________________


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