SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
Do Now:
1)
2)
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SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
Definition
Identifying and Evaluating Exponential Functions
1) Does each table represent a linear or an exponential function? Explain.
a)
b)
c)
d)
2
SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
Evaluating Exponential Functions
2)
c.
3
SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
Sketching and Exploring Exponential Functions (a > 0, b > 0)
3) Graph the function.
x
-2
-1
0
1
2
3
4
y
y​  1​(​2​)​ x​
(x, y)
a) Is the graph exponential growth or decay? How do you know?
___________________________________
b) Is this an increasing or decreasing function? Explain
__________________________________________
c) Will the graph ever cross the x-axis? _____________________________________
d) State the domain ____________________________ State the range
_______________________________
e) What is the y-intercept?_____________________________
f) What is the growth factor?___________________________
An exponential function
is called a growth function when b > 1.
An asymptote is a line that a function gets close to but never crosses. For exponential functions, the x-axis
is an asymptote.
4
SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
Sketching and Exploring Exponential Functions (a > 0, 0< b < 1)
4)
y​  2​(​0​.​4​)​ x​
x
y
(x, y)
a) Is the graph exponential growth or decay? How do you know?
___________________________________
b) Is this an increasing or decreasing function? Explain
__________________________________________
c) Will the graph ever cross the x-axis? _____________________________________
d) State the domain ____________________________ State the range
_______________________________
e) What is the y-intercept?_____________________________
f) What is the decay factor?___________________________
An exponential function
is called a decay function when 0< b < 1. In other words, b is a fraction or a decimal between 0 and 1.
An asymptote is a line that a function gets close to but never crosses. For exponential functions, the x-axis
is an asymptote.
5
SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
Practice:
1) Graph the function:
x
-3
-2
-1
0
1
2
3
y
y​  2​(​3​)​ x​
(x, y)
2) Graph the function.
x
-3
y
1​
y​  1​(​ )​ x​
2​
(x, y)
-2
-1
0
1
2
3
6
SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
LESSON PRACTICE
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SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
LESSON PRACTICE
8
SWBAT: Identify and evaluate exponential functions. Graph exponential functions.
Lesson 9-2
LESSON PRACTICE ANSWERS
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