1. Is the graph an increasing or decreasing function? Explain your - - PowerPoint PPT Presentation

DAY 97 – EXPONENTIAL FUNCTIONS: DOMAIN & RANGE

EXAMPLE

Part I Using a graphing calculator, graph the function and sketch the graph on the grid provided below.

EXAMPLE

Part I Using a graphing calculator, graph the function and sketch the graph on the grid provided below.

• 1. Is the graph an increasing or decreasing

function? Explain your answer.

• 2. Trace or use the table feature on your calculator

to fill out the tables below. As the value of x gets very large, what happens to the value of 2x ?

x y 1 5 10 20

• 1. Is the graph an increasing or decreasing function?

Explain your answer. Increasing function as x increases, y increases

• 2. Trace or use the table feature on your calculator to

fill out the tables below. As the value of x gets very large, what happens to the value of 2x ?

x 2x 1 1 2 5 32 10 1024 20 1.048576x106

As the value of x gets very small, what happens to the value of 2x ?

x y

• 1
• 3
• 5
• 10
• 20

As the value of x gets very small, what happens to the value of 2x ?

x 2x

• 1

0.5

• 3

0.125

• 5

0.03125

• 10

9.765625x10-4

• 20

9.536743x10-7

• 3. Will the value of 2x ever equal 0? Explain your answer.
• 4. Are there any values of x that would make 2x undefined?

Explain your answer

• 5. State the domain and range for

Domain: Range:

x x f 2 ) ( 

• 3. Will the value of 2x ever equal 0? Explain your answer.

approaches 0

• 4. Are there any values of x that would make 2x undefined?

Explain your answer no.

• 5. State the domain and range for

Domain: x R Range: y > 0

x x f 2 ) ( 

Part II Using a graphing calculator, graph the function along with the graph of from Part I, and sketch the graph of on the grid provided below

x x f 3 ) (  x x f 2 ) ( 

Part II Using a graphing calculator, graph the function along with the graph of from Part I, and sketch the graph of on the grid provided below

x x f 3 ) (  x x f 2 ) ( 

1.Is the graph an increasing or decreasing function? Explain your answer increasing function as x increases y increases

• 2. As the value of x gets very large, what happens to the

value of 3x ? also gets large

• 3. As the value of x gets very small, what happens to the

value of 3x ? 3x gets very small

• 4. How does the graph of compare to the graph of ?

3x increases faster that 2x

• 5. a. Given the general form (where a > 1),

what effect does increasing the value of "a" have upon the graph?

• b. What effect does decreasing the value of "a" have upon

the graph?

x

a x f  ) (

• 5. a. Given the general form (where a > 1),

what effect does increasing the value of "a" have upon the graph? The larger the a, the faster the graph will rise

• b. What effect does decreasing the value of "a" have upon

the graph?

x

a x f  ) (

Part III Use a graphing calculator to graph the function along with the graph of from Part I, and sketch the graph of on the grid provided below.

x

x f ) 5 . ( ) ( 

x

x f ) 5 . ( ) ( 

x

x f 2 ) ( 

Part III Use a graphing calculator to graph the function along with the graph of from Part I, and sketch the graph of on the grid provided below.

x

x f ) 5 . ( ) ( 

x

x f ) 5 . ( ) ( 

x

x f 2 ) ( 

• 1. Is the graph an increasing or decreasing function?

Explain your answer.

• 2. Trace or use the table feature on your calculator to fill
• ut the tables below.

As the value of x gets very large, what happens to the value of (0.5)x ?

x (0.5)x 1 5 10 20

• 1. Is the graph an increasing or decreasing function?

Explain your answer. Decreasing, as x increases y decreases

• 2. Trace or use the table feature on your calculator to fill
• ut the tables below.

As the value of x gets very large, what happens to the value of (0.5)x ?

x (0.5)x 1 1 0.5 5 0.03125 10 9.765625x10-4 20 9.536743x10-7

As the value of x gets very small, what happens to the value of (0.5)x ?

• 3. Will the value of (0.5)x ever equal 0? Explain your

answer.

x (0.5)x

• 1
• 3
• 5
• 10
• 20

As the value of x gets very small, what happens to the value

• f (0.5)x ?
• 3. Will the value of (0.5)x ever equal 0? Explain your answer.

no, it will get very close, but never reach 0.

x (0.5)x

• 1

1

• 3

2

• 5

8

• 10

32

• 20

1024

• 4. Are there any values of x that would make (0.5)x

undefined? Explain your answer.

• 5. State the domain and range for

Domain: Range:

• 4. Are there any values of x that would make (0.5)x

undefined? Explain your answer. no, we are never dividing by 0.

• 5. State the domain and range for

Domain: x R Range: y > 0

• 6. How does the graph of compare to the graph
• f ?

x

x f ) 5 . ( ) ( 

x

x f 2 ) ( 

• 6. How does the graph of compare to the graph
• f ?

The graphs are reflected over the y-axis

x

x f ) 5 . ( ) ( 

x

x f 2 ) ( 

Part IV Use the graphing calculator to graph the function along with the graph of from Part III, and sketch the graph of on the grid provided below.

x

x f ) 8 . ( ) ( 

x

x f ) 8 . ( ) ( 

x

x f ) 5 . ( ) ( 

Part IV Use the graphing calculator to graph the function along with the graph of from Part III, and sketch the graph of on the grid provided below.

x

x f ) 8 . ( ) ( 

x

x f ) 8 . ( ) ( 

x

x f ) 5 . ( ) ( 

• 1. Is the graph an increasing or decreasing function?

Explain your answer.

• 2. As the value of x gets very large, what happens to the

value of (0.8) x ?

• 3. As the value of x gets very small, what happens to the

value of (0.8) x ?

• 1. Is the graph an increasing or decreasing function?

Explain your answer. Decreasing, as x increases y decreases

• 2. As the value of x gets very large, what happens to the

value of (0.8) x ? (0.5)x gets smaller

• 3. As the value of x gets very small, what happens to the

value of (0.8) x ? (0.5)x gets larger

• 4. How does the graph of compare to the

graph of ?

• 5. a. Given the general form (where 0 < a < 1),

what effect does increasing the value of "a" have upon the graph?

• b. What effect does decreasing the value of "a" have

upon the graph?

x

x f ) 8 . ( ) ( 

x

x f ) 5 . ( ) ( 

x

a x f  ) (

• 4. How does the graph of compare to the

graph of ? The graph (0.8) decreases slower that (0.5)x

• 5. a. Given the general form (where 0 < a < 1),

what effect does increasing the value of "a" have upon the graph? The higher the value or a closer a gets to 1, the more the graph will look like horizontal line where y=1

• b. What effect does decreasing the value of "a" have

upon the graph?

x

x f ) 8 . ( ) ( 

x

x f ) 5 . ( ) ( 

x

a x f  ) (

EXAMPLE

Sketch the graph of State the domain and range.

. 1 2 ) (  

x

x g

The graph of this function is a vertical translation of the graph f(x)=2x down one unit. Domain: (–∞, ∞) Range: (–1, ∞)

f(x) = 2x f(x) = 2x -1 y = –1

EXAMPLE

Sketch the graph of State the domain and range.

. 2 ) (

x

x g





The graph of this function is a reflection the graph f(x)=2x in the y-axis. Domain: (–∞, ∞) Range: (0, ∞)

f(x) = 2x f(x) = 2 - x