6.3Exponential Functions - Kent City School District · 2018. 1. 6. · So what do the graphs of...

January 25, 2018

6.3Exponential Functions

exponential . . . has a variable for an exponentfunction . . . a relationship where each input has exactly one output

According to the rule, is a geometric sequence an exponential function?

Think about some of the example we looked at yesterday . . .750, 150, 30, 6, . . . -3, -6, -12, -24, . . . 4, 6, 9, 13.5, . . .Are exponential functions Linear?

Yes, the first term is a non zero constant, the common ratio is larger than zero and not equal to one, and n -1 is a variable exponent

No, there is not a common difference or constant rate of change. The change is proportional.

What are some of the characteristics of the graph of an exponential function?

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Copy and complete each table for the given exponential functions. In each table, what do you notice about the values of y?

y = 4(2)xx x y = 4( )x2 1 Sketch the graphs of the functions

given. How are the graphs similar? How are they different?

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Does the table represent a linear or an exponential function? Explain.

Evaluate the function when x = −2, 0, and

3. y = 2(9)x 4. y = 1.5(2)x

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Complete each table.

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Evaluate each function for the domain 0, 1, 2

y=2x y=0.8x y=2(4x)

y=10(3x) y=25(5x) y=(1/4)8x

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So what do the graphs of exponential functions look like . . .

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6.3 Desmos Explorationy = a(r)(bx + h) + k

a

k

h

b

r

translates up or down

translates left or right

vertical stretch/shrink scale factor

horizontal stretch/shrink scale factor

steepness

first term

common ratio

-a reflect over x - axis

-b reflect over y - axis

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Graph and compare each function. Define the domain and range. y = 3x y = -3x y = x y = x

x y

-2

-1

0

1

2

x y

-2

-1

0

1

2

x y

-2

-1

0

1

2

x y

-2-1

0

12

3 1

3 -1

y = 3 -x y = -3-x

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y = 3x y = 2(3)x

y = 2( x) y = 2( )x

x y

-2

-1

0

1

2

x y

-2

-1

0

1

2

x y-2-101

2

x y

-2-1

0

12

3 1

3 -1

Graph and compare each function. Define the domain and range.

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Graph f (x) = 4(2)x. Compare the graph to the graph of the parent function. Describe the domain and range of f.

Graph Compare the graph to the graph of the parent

function. Describe the domain and range of f.

Graph the function. Compare the graph to the graph of the parent function. Describe the domain and range of f.

5. f (x) = −2(4)x 6. f (x) = 2

Graph y = 4(2)x − 3 + 2. Describe the domain and range.

Graph the function. Describe the domain and range.

7. y = −2(3)x + 2 − 1 8. f (x) = (0.25)x + 3

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y = a bxa y-interceptb growth/common ratio

Write an exponential function that represents the bacteria population.

Find the bacteria population after 12 hours.

Find the bacteria population after 5 days.

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Pg 310: 1-42e, 46-50e, 51, 57