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Algebra 2: Lesson 10-1:
Read Lesson 10-1 and complete the notes as you read pgs. 523-527.
y = 2x
Exponential Functions -
Label the base and the exponent
Ex. 1: Sketch the graph of y = 2x . Then state the Domain and Range.
x
-3
-2
-1
0
½
1
2
3
y = 2x
**What is happening as the value
of x decreases? ___________
___________________________________
Domain ___________
Range _______________
Your Turn:
Graph y = 4x Then state the domain and range.
x
-3
-2
-1
0
½
1
2
3
y = 4x
**What is happening as the value
of x decreases? ___________
___________________________________
Domain ___________
Range _______________
Exponential Function - _______________________________________________________________
What are the characteristics of an exponential function?
1. _______________________________________________________________________________
** What does it mean if a graph is continuous?
2. _________________________________________________________________________________
3. _________________________________________________________________________________
**What is an asymptote? And what does it mean if the x-axis is the asymptote of an
exponential function?
4. _________________________________________________________________________________
5. _________________________________________________________________________________
**What is the y-intercept?
6. ___________________________________________________________________________________
Exponential Growth - ______________________________________________________________
Exponential Decay - _______________________________________________________________
**What is the base of an exponential growth function???
**What is the base of an exponential decay function???
Ex. 2: Determine whether each function represents exponential growth or decay. Be able to defend your
answer.
a)
y = (1/5)x
b)
y = 3(4)x
c)
y = 7(1.2)x
**Why is ‘4’considered the base
and not ‘12’???
**Think: 4 is the only number
being raised to an exponent . . .
Your Turn: Determine whether each function represents exponential growth or decay.
d)
y = (0.7)x
e)
y = ½ (3)x
f)
y = 10(3/4)x
Exponential Equations and Inequalities:
Ex. 4: Simplify each expression:
5
 2 3 = _______________
a)
2
b)
(7 2 )
**Think: x3 • x4 = x7
because we added the exponents
since the bases were the same
**So, if the bases are the same, add the exponents. Remember, to add radicals, the
radicands (3 below the radical sign) must be the same.
3
 _________
**Think: (x4)2 = x8
because we multiply the exponents
**So if a power is raised to a power, then multiply the exponents. Remember, to multiply
radicals, just multiply the radicands, and multiply any numbers outside the radical sign.
Your Turn: Simplify each expression:
c)
5
3
5
2
 __________
**Think: if bases are the same, what do we do to the exponents
when dividing??????
d)
(6 5 )
6
 ________
Property of Equality for Exponential Functions:
If b is a positive number other than 1, then bx = by if and only if x = y
Example:
If 2x = 28, then x = 8.
**Bases are the same . . . then the exponents are equal.
Ex. 5: Solve each equation:
(walk through each problem using the example in the textbook)
a) 32n + 1 = 81
81 = 3 4
**What can we do to make
like bases????
Replace 81 with 34
b)
42x = 8x – 1
4 = 22 AND 8 = 23
Your Turn: Solve each equation:
c)
49n – 2 = 256
d)
35x = 92x – 1
**What can we do to make
the bases the same?????
You now have like bases
Exponential Inequalities:
If 5x < 54, then x < 4.
If 5x > 54, then x > 4.
Ex. 6: Solve 43p – 1 > 1/256
Like bases . . . 256 = 44 and if 256 is in the denominator, then
the exponent is negative.
Your Turn: Solve 53 – 2k > 1/625
Homework: pg. 528: 21, 22, 27-32, 39, 41, 42, 44, 45, 46, 47,51