Honors Algebra 2 Spring 2014 Name__________________________

NC. Objectives to be covered:1.01 Simplify and perform operations with rational exponents and logarithms to solve problems. .2.07 Use equations with radical expressions to model and solve problems: a. Solve using graphs. a. Interpret the degree, constants, and coefficients in the context of the problem.

Day

Date Lesson Assignment

1 Mon.4/7

Review for Unit 4 TestRadicals and Conjugates(7.1-7.3) STUDY for Unit Test 4

Polynomial Functions

Tues.4/8 Unit Test 4: Polynomial Functions Unit 5: Packet p. 2

2 Wed.4/9

Fractional Powers and RootsClasswork: Packet p.3 & 4

Packet p. 5 (Part 1: EVEN)All of Part 2 and Part 3

3 Thurs.4/10

Section 7.5: Solving Radical Equations with one and two

radicals: checking for extraneous solutions

Packet p. 6

4 Fri.4/11

Section 7.7 & 7.8: Inverse Relations & Functions: Find

the inverse, graph, and find the domain and range of the function

and its inverse

Classwork: Packet p. 7Homework: Packet p. 8

Watch video on Function Operationshttp://www.youtube.com/watch?v=5934UqzXvKA

5 Mon.4/14

Review for Quiz on Radical Functions(MATHO)

Intro to Function OperationsNotes: Packet p. 2

Watch video on Composition of Functions http://www.youtube.com/watch?v=S4AEZElTPDo

Revised Packet p. 9

6 Tues.4/15

Quiz on Radical FunctionsComposition of Functions(Notes p.

3)Discovery education video

Packet p. 10Part 1

7 Wed.4/16

Composition of Functions ( packet p. 4)

Review for the Unit Test 5Packet p. 10 Part 2

Packet p. 11(answers on packet p. 12)

8 Thurs.4/17

Unit Test 5: Radical Functions

Packet p. 13 & 14Print notes and packet for Unit 6

Radicals and Conjugates1

Homework Grade:

Find each root.1. 2.

Simplify each radical expression.

3. 4. 5.

Rationalizing the denominator:

6. 7.

Simplify.8.

9.

10.

11.

12.

2

Honors Algebra 2 Spring 2014 Name__________________________ Classwork Part 1: Using the QR code below, do the problems on the website. Write the problem and show your work. Check your answer when you finish the question.

1. 2. 3.

4. 5. 6.

7. 8. 9.

10. 11.

Classwork Part 2: Solve the problem. Where is the mistake?

3

HOMEWORK: (Part 1)

4

Honors Algebra 2 Spring 2014 Name__________________________

Part 2: Write each expression in radical form.

1. 2. 3.

Part 3: Write each expression in exponential form.1. 2. 3.

Solving Radical Equations

5

1.) 2.)

3.) 4.)

5.) 6.)

7.) 8.)

9.) 10.)

11.) 12.)

13.) 14.)

15.) The velocity of a free-falling object is given by where h is the distance in feet the object has fallen and g is acceleration due to gravity in feet per second squared. The value of g depends on your altitude. If an object hits the ground with a velocity of 25 feet per second, from what height was it dropped in each of the following situations?

a.) You are standing on earth, so g = 32 ft/s2.b.) You are on a space shuttle, so g = 29 ft/s2.c.) You are on the moon, so g = 0.009ft/s2.

Classwork: Using the QR code, answer the following. Show work. Do problems #1-10

6

Honors Algebra 2 Spring 2014 Name__________________________

1. 2.

3. 4.

5. 6.

7. 8.

9. 10.

Homework: Find the inverse of each function.

Complete the chart below. Find the inverse and the domain and range of the function and its inverse. Determine whether the inverse is a function.Problem Domain(interval notation) Range(interval notation) Is f-1 a function?1.

f-1(x)=

2.

7

f-1(x)=

3.

f-1(x)=

4.

f-1(x)=

5.

f-1(x)=

6.

f-1(x)=

7.

f-1(x)=

Part 2: The formula for converting from Celsius to Fahrenheit temperatures is

. b. Find the inverse of the formula. Is the inverse a function?

b. Use the inverse to find the Celsius temperature that corresponds to 20˚F.

8

Honors Algebra 2 Spring 2014 Name__________________________ Packet Page 9-Homework Day 5

Homework Day 6-Packet Page 10-Part 1

9

Homework Day 7-Packet Page 10-Part 2

Composition and Applications

Review for Unit Test 51. Simplify: 163/2

2. Graph: f(x)=10

Honors Algebra 2 Spring 2014 Name__________________________ 3. Simplify:

4. Find the inverse of y = 6x + 4

5. Give the domain and range of .

6. Simplify:

7. Let f(x)=3x. Find the inverse.

8. Simplify:

9. Solve: . Check for extraneous solutions.

10.Evaluate: 32-2/5

11.Simplify:

12.Sketch the graph of f(x)= -x2 + 3. Is the inverse a function?

13.Solve: 6x2/3 =24. Check for extraneous solutions.

14.Are f and g inverses?

15.Solve: . Check for extraneous solutions.

16.Let f(x) = 2x+3. Find f-1.

17.Simplify: .

18.Describe how to obtain the graph of from the graph of

Unit 5 ~ Practice Test ANSWER KEY!

1.) 64 2.)

11

3.)

4.)

5.) Domain: Range:

6.)

7.)

8.)

9.) y = 215

10.)

11.)

12.) No

13.) x = 8 & -8

14.) Yes

15.) x = 8

(x = -7 is an extraneous solution)

16.)

17.)

18.) Left 3 units & Down 2 units

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Honors Algebra 2PROBLEM SET MUST SHOW ALL NECESSARY WORK FOR CREDIT!!!!!!

__________1. If 3+2 i is a solution for x2 + bx +c = 0, where b and c are real numbers, what is the value of b?

A. -13 B. -6 C. 6 D. 13

__________2. With respect to which line is the graph of f(x) = x4 – 3x2 + 6 symmetric?

A. x = 6 B. y = 0 C. y = x D. x = 0

__________3. What are the zeros of f(x) = x4 – 7x3 + 15x2 – 9x ?

A. {1, 3} B. {0, 1} C. {0, 1, 3} D. {0, 1, 2, 3}

__________4. A model rocket is fired upward at an initial velocity of v0 of 240 ft/s. The height h(t) of the rocket is a function of time t in seconds and is given by the formula: h(t) = v0t – 16t2. How long will it take the rocket to hit the ground after takeoff?

A. 16 s B. 15 s C. 7.5 s D. 4 s

__________5. What are the approximate solutions of 6x2 – 8x + 1 = 0?

A. {0.14, 1.19} B. {-0.19, -2.14} C. {-0.14, -1.19} D. {0.19, 2.14}

__________6. What is the approximate positive zero of P(x) = 2x4 – 5x – 16 ?

A. 2.01 B. 1.97 C. 1.89 D. 1.75

__________7. A company’s total revenue R (in millions of dollars) is related to its expenses by the equation R = 4x3 – 16x2 + 12x, where x is the amount of expenses (in tens of thousands of dollars). What values of x will produce zero revenue?

A. x = 0, x = 1, x = 3 B. x = 1, x= 3, x= 4 C. x =1, x=3 D. x =0, x = -1, x = -3

__________8. Which quadratic equation has roots 2+√5 , 2−√5 ?

A. x2 + 4x + 1 = 0 B. x2 - 4x – 1 = 0C. x2 – 4x + 1 = 0 D. x2 + 4x – 1 = 0

___________9. What are the factors of x4 – 25x2 + 144?

__________10. Which expression is the factored form of x3 + 2x2 – 5x - 6 ?

A. (x + 1)(x + 1)(x – 6 ) B. (x + 2)(2x – 5 )(x – 6 )C. (x + 3)(x + 1)(x – 2 ) D. (x – 3)(x – 1 )(x + 2)

__________11. What is the approximate distance between (-7, -3) and (9 , 8) ?

A. 5.4 B. 11.2 C. 16.8 D. 19.4

___________12. Graph f(x) = x4 – 4x2 + 4?

13

x

y

Graph for # 20

_________13. What are the real zeros for f(x) = x3 – 3x2 + 8 ? (Approximate the zeros to the nearest tenth)

A. –1 B. –2 C. –1.4 –1.5

__________14. Use synthetic substitution to find f( -2) for f(x) = 2x4 –3x3 –4x + 12.

A. 15 B. 67 C. –53 D. 3 E. 76

__________15. One factor of x3 – 3x2 – 4x + 12 is x + 2. What are the other two factors?

A. x + 2, x + 3 B. x + 2, x – 3 C. x – 2 , x + 3 D. x – 2 , x – 3

__________16. Solve x4 – 6x2 – 27 = 0.

A. ±3 i ,±√3 B. 3 , √3 C. ±3 , ±i√3 D. ±3

__________17. Which value is NOT a solution of x4 – 3x2 – 54 = 0?

A. –3 B. 3 C. –3i D. −i √6

__________18. What is the relative maximum for f(x) = x3 + 2x2 - 12x - 24 .

A. –2.77 B. 3.33 C. 1.44 D. –34.15

__________19. If f(x) = 2x2 + x and g(x) = x – 2 , what is [f ∘ g](x) ?

A. 2x2 –7x + 6 B. 2x2 –7x + 8 C. 2x2 –3x +2 D. x2 –3x + 6

__________20. The graph of a cubic function of the form y = ax3 + b is shown. What can you determine about the values of a and b?

A. a > 0, b > 0 B. a > 0, b < 0 C. a < 0, b > 0 D. a < 0, b < 0

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