UNIT 4: “POWER TRIP” Standard 4.1: demonstrate understanding of the properties of

exponents and to graph exponential functions (11-1, 11-2) Standard 4.2: solve problems using exponential functions

(11-2) Standard 4.3: use the natural number e to solve problems (11-3) Standard 4.4: demonstrate understanding of the properties of

logarithms (11-4) Standard 4.5: use common and natural logarithms to solve

problems (11-5, 11-6) Modeling Data

Warm-up: On your calculators, graph…

How are these graphs alike? How are they different? What conclusions can I draw about the key

characteristics of this type of graph?

Use MATH terminology in your descriptions.

You know…stuff like: domain, range, continuity, intercepts, asymptotes, behavior over intervals…yeah, stuff like that!

2 3 5 10x x x xy y y y

Check it out!!!…Graph the following equations:

Compare and contrast the graphs. How are they alike? Different?

Use MATH terminology in your descriptions.You know…stuff like: translation, reflection,

vertical, horizontal, x-axis, y-axis, parent graph, etc.

21. 6 2. 6 3 3. 6 4. 6x x x xy y y y

STANDARD 4.1: DEMONSTRATE UNDERSTANDING OF THE PROPERTIES OF EXPONENTS AND TO GRAPH EXPONENTIAL FUNCTIONS (11-2)

The essential questions are…What will happen if my variable is the

exponent instead the base?Can exponential behavior be predicted?What sorts of problems can be solved using

exponential functions in real life?

EXPONENTIAL FUNCTIONS:Functions in which there is a variable acting as

an exponent.The base will be some real number.

What are the key characteristics of an exponential function? (from warm-up)

2xy

Review Warm-up …TRANSFORMATIONS!!!

26 6 3 6 6x x x xy y y y

LOOK AT THESE GUYS…What’s going on?

14

4

xxy y

Graph these…

21. 3 4 2. ( ) 4

3. 2 4. ( ) 5 2

x x

x x

y f x

y f x

STANDARD 4.1: DEMONSTRATE UNDERSTANDING OF THE PROPERTIES OF EXPONENTS AND TO GRAPH EXPONENTIAL FUNCTIONS (11-1)

The essential questions are…What affect does a power have on a number?How do exponents behave when their bases are

added or subtracted? Multiplied? Divided? Raised to a power?

What does it mean when a base has a negative exponent? A fractional exponent? An irrational exponent?

WHAT EFFECT DOES A POWER HAVE ON A NUMBER?

where is an integer.nb b

HOW DO EXPONENTS BEHAVE WHEN THEIR BASES ARE ADDED OR SUBTRACTED?

2 2 2 2

2 3 2 2

4 3 9

5 3 6 7x 2 4 3

x x x y

x x x x x

HOW DO THEY BEHAVE WHEN THEIR BASES ARE MULTIPLIED?

5 3 2 41. ( ) 2. (5 )( 7 )x x z xz

DIVIDED?

2 54 7

6 2 4

3 (3 )1. 2.

3 ( )x yx

WHAT ABOUT NEGATIVE EXPONENTS?

22 1

33 22

1. 4 4

2. What is diff erent between

3 and 3 ?ff

TRY SOME…

14 2

5

2 534 7

42 3

2 2 31. 2.

2 4

3. 4. x y

s tx y

WHAT IF MY EXPONENT IS NOT AN INTEGER?

1

n

m

n

b

b

SOLVING EQUATIONS INVOLVING RATIONAL EXPONENTS.

OKAY…WHAT IF MY EXPONENT IS NOT RATIONAL?

26

SOLVING EQUATIONS5

2724 15 12a

SAGE AND SCRIBE.One piece of paper per partnership.One person does the thinking - Sage, the other

writes - Scribe.Sage must tell the scribe exactly what to do but

may not write anything. The sage must describe with words only.

Scribe writes exactly what the Sage tells them to write.

For next problem switch roles.

SAGE AND SCRIBE.p A46 Lesson 11-1 #1 – 19 odd

TOD:1) How do exponential functions differ from

linear or polynomial functions?

2) Draw the parent graph for an exponential function. Label all important characteristics and discuss it behavior over the course of its domain and its end behavior.

HOMEWORK:4.1: p 700 #21 – 67 every other odd, 714.1: p709 #11 – 21 odd