Graph the Following Exponential Functions:

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Exercise 1

f(x) = { 3 }^{ x }

Exercise 2

f(x) = { (\frac { 2 }{ 5 }) }^{ x }

Exercise 3

f(x) = { (\frac { 3 }{ 2 }) }^{ x }

Graph the Following Logarithmic Functions:

Exercise 4

f(x)= \log_{ 2 } x

Exercise 5

f(x)= \ln { x }

Exercise 6

f(x)= \log_{ \frac { 1 }{ 2 } } x

Exercise 7

f(x)= \log_{ \frac { 1 }{ 4 } } x

Graph the Following Trigonometric Functions:

Exercise 8

f(x)= \cos { (x + \frac { \pi }{ 2 }) }

Exercise 9

f(x)= \sin { 2x }

 

 

Solution of exercise 1

Graph the exponential function:

f(x) = { 3 }^{ x }

x -3 -2 -1 0 1 2 3
f(x) = { 3 }^{ x } \frac { 1 }{ 27 } \frac { 1 }{ 9 } \frac { 1 }{ 3 } 1 3 9 27

 

Solution of exercise 2

Graph the exponential function:

f(x) = { (\frac { 2 }{ 5 }) }^{ x }

x -3 -2 -1 0 1 2 3
f(x) = { (\frac { 2 }{ 5 }) }^{ x } 15.625 6.25 2.5 1 0.4 0.16 0.064

 

Solution of exercise 3

Graph the exponential function:

f(x) = { (\frac { 3 }{ 2 }) }^{ x }

x -3 2 -1 0 1 2 3
f(x) = { (\frac { 3 }{ 2 }) }^{ x } \frac { 27 }{ 8 } \frac { 9 }{ 4 } \frac { 3 }{ 2 } 1 \frac { 2 }{ 3 } \frac { 4 }{ 9 } \frac { 8 }{ 27 }

 

Solution of exercise 4

Graph the logarithmic function:

f(x)= \log_{ 2 } x

x \frac { 1 }{ 8 } \frac { 1 }{ 4 } \frac { 1 }{ 2 } 1 2 4 8
f(x)= \log_{ 2 } x -3 -2 -1 0 1 2 3

 

Solution of exercise 5

Graph the logarithmic function:

f(x)= \ln { x }

x 0.1 0.5 1 2 3 4 5
f(x)= \ln { x } -2.3 -0.7 0 0.7 1.1 1.4 1.6

 

Solution of exercise 6

Graph the logarithmic function:

 f(x)= \log_{ \frac { 1 }{ 2 } } x

x \frac { 1 }{ 8 } \frac { 1 }{ 4 } \frac { 1 }{ 2 } 1 2 4 8
 f(x)= \log_{ \frac { 1 }{ 2 } } x 3 2 1 0 -1 -2 -3

 

Solution of exercise 7

Graph the logarithmic function:

 f(x)= \log_{ \frac { 1 }{ 4 } } x

x 1/8 \frac { 1 }{ 4 } \frac { 1 }{ 2 } 1 2 4 8
 f(x)= \log_{ \frac { 1 }{ 4 } } x \frac { 3 }{ 2 } 1 1/2 0 -\frac { 1 }{ 2 } -1 - \frac { 3 }{ 2 }

 

Solution of exercise 8

Graph the trigonometric function:

f(x)= \cos { (x + \frac { \pi }{ 2 }) }

 

x 0 \frac { \pi }{ 4 } \frac { \pi }{ 2 } \frac { 3 \pi }{ 4 } \pi \frac { 5 \pi }{ 4 } \frac { 3 \pi }{ 2 } \frac { 7 \pi }{ 4 } 2 \pi
f(x)= \cos { (x + \frac { \pi }{ 2 }) } 0 -0.7 -1 -0.7 0 0.7 1 0.7 0

 

Solution of exercise 9

Graph the trigonometric function:

f(x)= \sin { 2x }

x 0  \frac { \pi }{ 4 } \frac { \pi }{ 2 } \frac { 3 \pi }{ 4 } \pi \frac { 5 \pi }{ 4 } \frac { 3 \pi }{ 2 } \frac { 7 \pi }{ 4 } 2 \pi
f(x)= \sin { 2x } 0 1 0 -1 0 1 0 -1 0

 

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Hamza

Hi! I am Hamza and I am from Pakistan. My hobbies are reading, writing and playing chess. Currently, I am a student enrolled in the Chemical Engineering Bachelor program.