algebra 2 and trigonometry - white plains public schools...2 table of contents day 1: chapter...
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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
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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
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Teacher Modeled Student Try It!
(√ )
(√ )
(√ )
(√ )
Concept 2: Rewrite each in radical form.
Teacher Modeled Student Try It!
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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!
( )
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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)
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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) =
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Example 11
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Challenge
SUMMARY
Exit Ticket
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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.
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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.
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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.
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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 (
)
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Challenge
Summary/Closure
Exit Ticket
24
Day 6 – Review of Exponential Functions
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c.
d.
26
27
48. Explain each transformation below from y = .
a) y = ________________
b) y = ________________
c) y = ________________
d) y = ________________
e) y = ________________
f) y = (
)
________________
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HW ANSWERS
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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