1. No category

unit 6 lesson 1 notes.notebook
Warm Up
April 16, 2015
I. Introduction to Exponentials
Check the seating chart at the front. The general form of an exponential function is ___________________________.
1. ___x_______ is the _________exponent_________________________
2. ____a_____ is the _____initial amount (start) ‐ y‐intercept_____
Get your unit 6 assignment sheet and lesson 1 note packet.
3. ____b______ is the __base (growth/decay)_________________
Apr 15­3:01 PM
Exponential functions can represent exponential _____growth_______________ or exponential ___decay_________________.
Apr 15­3:02 PM
Examples: Classify each as exponential growth or decay then identify
the y‐intercept as well as the growth or decay factor.
growth, (0, 4)
1. 1.
Exponential _____growth_________ occurs when __________b > 1__________
2.
Exponential _______decay______ occurs when ______0 < b < 1_________
decay, (0, 24)
2. 3. growth, (0, 1)
4. growth b>1 (b =3)
decay, 0 < b < 1
decay, (0, 100)
5. growth, (0, 12)
Apr 15­3:04 PM
Apr 15­3:04 PM
II. Parent Graph for Exponential Functions
Exponential Growth:
Exponential Decay:
GRAPH x
‐3
‐2
‐1
0
y­intercept: (0, a)
y­intercept: (0, a)
1
2
x­intercept: none
x­intercept: none
3
y
0.125
0.25
0.5
1
2
4
8
y­int (0, 1)
x­int : none
domain: all reals
domain: all reals
d: all reals
range: y > 0
range: y > 0
r: y > 0
asymptote: y = 0
asymptote: y = 0
asymptote: y = 0
Apr 15­3:05 PM
Apr 15­3:06 PM
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unit 6 lesson 1 notes.notebook
April 16, 2015
GRAPH
asymptote
x
Exponential functions have ONE _______________________________. Asymptotes are lines that the function cannot touch or cross. They are
like walls that the function gets closer and closer to, but never reaches. Exponential functions only have _________________________ asymptotes. We write the equation of a horizontal asymptote as ___________________.
y
8
4
2
1
0.5
0.25
0.125
‐3
‐2
‐1
0
1
2
3
1
y = #
Answer the following questions about the parent graph
none exists write none.
, if
y=0
, is ________________________
all reals
y > 0
is __________________________________________
c) Range for
(0, a)
d) y‐intercept(s) is _____________________________________________
none
e) x‐intercept(s) is _____________________________________________
a) Horizontal asymptote for
b) Domain for
y­int (0, 1)
x­int : none
is _________________________________________
d: all reals
r: y > 0
asymptote: y = 0
Apr 15­3:07 PM
Apr 15­3:09 PM
II. Graph Form
Signiicance of h ­ Signiicance of a ­ x‐h: ____
move right h units________________________________________________________________________ a is negative:
________________________________________________________________________________
________________________
reflects the x­axis
move left h units________________________________________________________________________
x+h: ______
Signiicance of k – 0<a<1: ________________________________________________________________________________
______________________________ vertical shrink
vertical stretch
moves up k units_________________________________________________________________________________ +k: _________
moves down k units_____________________________________________________________________________
‐k: _________
a>1:
________________________________________________________________________________
__________________________________
Apr 15­3:09 PM
Apr 15­3:10 PM
1. a) Explain the transformation of the parent graph
reflected x­axis
y = 0
_____________________________________________________________________
a) Horizontal Asymptote _________________
all reals
y < 0
b) Domain ______________________ c)Range_________________________
(0, ­1)
none
d) x‐intercept(s) ________________ e) y‐intercept(s) ________________
up 5
y = 5
all reals
y > 5
none
(0, 6)
Apr 15­3:10 PM
Apr 15­3:12 PM
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unit 6 lesson 1 notes.notebook
April 16, 2015
Apr 15­3:13 PM
Apr 16­1:36 PM
Apr 16­12:16 PM
Apr 16­1:37 PM
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