algebra 2 and trigonometry - white plains public schools...2 table of contents day 1: chapter...

1

Algebra 2 and

Trigonometry

Chapter 7: Exponential Functions

Name:______________________________

Teacher:____________________________

Pd: _______

2

Table of Contents

Day 1: Chapter 7-1/7-2: Laws of Exponents

SWBAT: Simplify positive, negative, and zero exponents. Pgs. 3 – 5 in Packet

HW: Page 289 #’s 3 – 25 odd

Pages 292 – 293 #’s 3 – 9 odd, 17, 18, 19, 22, 30, 32, 35 – 75 eoo

Day 2: Chapter 7-3: Rational Exponents

SWBAT: simplify rational exponents. Pgs. 6 – 10 in Packet

HW: Pages 296 – 298 #’s 3, 5, 6, 18, 19, 22, 32, 39 – 81 eoo

Day 3: Chapter 7-4: Exponential Functions

SWBAT: Graph Exponential Functions

Pgs. 11 – 15 in Packet

HW: Pages 302 – 303 #’s 3, 4, 7-9

QUIZ

Day 4: Chapter 7-5: Exponential Equations

SWBAT: Solve Exponential Equations

Pgs. 16 – 18 in Packet

HW: Page 305 #’s 1- 19 odd, 12, 23

Day 5: Chapter 7-6: Exponential Equations

SWBAT: Solve Exponential Equations with like and unlike bases

Pgs. 19 – 23 in Packet

HW: Pages 307- 308 #’s 3, 8, 9, 10, 15 – 35 odd

Day 6: Review

SWBAT: Solve Problems involving Exponents

Pgs. 24 – 27 in Packet

HW: Finish this section in the packet

HOMEWORK ANSWER KEYS – STARTS AT PAGE 28

3

Day 1: Laws of Exponents

SWBAT: Simplify positive, negative, and zero exponents.

Warm – Up: Exponent Rules

Concept 1: Simplifying Exponents

LAWS of EXPONENTS: Test Question A. thru H.

#1. = ________ 1A. = ________

#2.

= ________ 2B. _______

5

12

x

x

#3. ( )y =

3C. ________43 x

#4. ( ) = _______ 4D. ( ) = _______

#5. (

)

= ________ 5E. (

)

= ________

Multiplication: Ex. x2 x

5 =

Division:

=

Ex.

=

Raising to a Power: (xa)b = x

ab Ex. (x

5)3

=

Power of a Product: (xy)a = x

a y

a Ex. ( )3 =

Power of a Quotient: a

aa

y

x

y

x

Ex. (

)

=

4

Zero and Negative Exponents

LAWS of EXPONENTS: Test Questions

#6. 0;______0 xx 6F. = _______

( ) = _______ = _______

Ex. 1) Write 2

34

ab

bawith only positive exponents.

2) Write with only positive exponents.

3) Write the following with only positive exponents:

a) 52

23 )(

xy

y b)

4) Simplify each.

a) 57

34

3

6

yx

yx

b)

Zero exponents: 01 xx

x

xand

x

x nn

n

n

n

n

, so x

0 = 1

Negative Exponents: x- n

= nx

1 and (

)

= (

)

5

Challenge Problem: Simplify. Use only positive exponents.

Summary/Closure:

Exit Ticket

6

Day 2: Rational Exponents

SWBAT: Simplify rational exponents.

Warm - Up:

Rational Exponents

Exponential Form Radical Form

= ( √ )

Concept 1: Rewrite each in exponential form.

Teacher Modeled Student Try It!

(√ )

(√ )

root

power

xThink : = root powerx or

7

Teacher Modeled Student Try It!

(√ )

(√ )

(√ )

(√ )

Concept 2: Rewrite each in radical form.

Teacher Modeled Student Try It!

8

Use exponents to write the radical expression. Let the variable represent positive numbers.

Teacher Modeled Student Try It!

√

√

√

√

Write the given expression, using a radical sign. Let the variables represent positive numbers

Teacher Modeled Student Try It!

( )

9

Practice:

1. If f(x) = 2

3

x , find f(16).

2. Evaluate

3.

10

Challenge

Summary/Closure

Exit Ticket:

11

Day 3 - Exponential Functions

SWBAT: Simplify rational exponents.

Warm - Up:

12

An exponential function is of the form y = b 0, b 1, and x is a real number. Domain = {x∣x Real numbers}

Range = {y∣y }

Example 2: Graph y = (

)

, y = on the graph below.

Observations from above:

(1) (2) (3)

13

Shifting the basic Exponential Graph f(x) =

Transformation Transformation up down left right Reflect over x-axis Reflect over y-axis

In examples 1 – 6, write an equation for each translation of y =

1. 2 units up __________________

2. 1 units down __________________

3. right 4 units __________________

4. left 3 units __________________

5. 1 units up, 4 units left __________________

6. 3 units down, 5 units right ________________

7. f(x) = means ________________

8. f(x) = (

)

means ________________

9. Graph f(x) = 10. Graph f(x) =

14

Example 11

15

Challenge

SUMMARY

Exit Ticket

16

Day 4 - Exponential Equations

SWBAT: solve equations involving exponents.

Warm-Up: 1) What is the multiplicative inverse of ?3

2

2) What is the multiplicative inverse of ?3

1

_____________________________________________________________________________

To solve an equation involving exponents: Ex.

1. Write the equation with only the variable term 1.

on one side of the equation.

2. Divide both sides of the equation by the coefficient 2.

of the variable term.

3. Raise both sides of the equation to the power that is 3.

the reciprocal of the exponent of the variable.

4. Simplify the right side of the equation. 4.

5. Check the solution.

xxxx aa

aa

1

11

17

Concept - Solve for x in each exponential equation:

Teacher Modeled Student Try It!

√

√

18

Challenge

Summary/Closure

Exit Ticket:

19

Day 5 - Exponential Equations involving like/unlike bases

SWBAT: Solve Exponential Equations with like and unlike bases

Warm-Up:

1) Express 36 as a power.

2) Express 81 as a power.

3) Express 32 as a power.

Concept 1: Solving Exponential Equations with the like Bases

If the bases are equal, the exponents must be equal.

Ex. Solve for x: 3x = 3

2x-2

To solve an equation with like bases: Ex.

1. Write the equation. 1.

2. Since the bases are alike, equate the exponents. 2.

3. Solve the resulting equation. 3.

20

Concept 1 - Solving Exponential Equations with the like Bases

Teacher Modeled Student Try It!

(

)

(

)

Concept 2: Solving Exponential Equations with Different Bases

If possible, write each term as a power of the same base.

Solve for x and check: 22x

= 8

To solve an equation with unlike bases: Ex.

1. Write the equation. 1.

2. Change the “higher” base to a power of the smaller base. 2.

3. Simplify the “higher” base. 3.

4. Since the bases are alike, equate the exponents. 5.

5. Solve the resulting equation. 5.

21

Concept 2 - Solving Exponential Equations with the unlike Bases

Teacher Modeled Student Try It!

Concept 3: Solving Exponential Equations with Different Bases (neither base is the power of

the other)

If possible, write each term as a power of the same base.

Solve for x and check: 9x+1

= 27x

To solve an equation with unlike bases: Ex.

1. Write the equation. 1.

2. Change each base to a power of the same number. 2.

3. Simplify each base. 3.

4. Since the bases are alike, equate the exponents. 5.

5. Solve the resulting equation. 5.

22

Concept 3 - Solving Exponential Equations with the unlike Bases(neither base is the power of

the other)

Teacher Modeled Student Try It!

5x-1 = (0.04)2x (

)

23

Challenge

Summary/Closure

Exit Ticket

24

Day 6 – Review of Exponential Functions

25

c.

d.

26

27

48. Explain each transformation below from y = .

a) y = ________________

b) y = ________________

c) y = ________________

d) y = ________________

e) y = ________________

f) y = (

)

________________

28

HW ANSWERS

29

Day 6 - REVIEW

c. d. y = (

)

48a. shift 2 right 48b. shift 2 down 48c. shift 4 right, up 7 48d. shift 1 left, down 8 48e. reflect over x-axis, up 1 48f. reflect y = 3-x over y-axis, shift 6 right