unit 4: “power trip” standard 4.1: demonstrate understanding of the properties of exponents and...
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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
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?
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
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.
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.
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