Question #182824

Explain how the graph of r(x)=-3tan(1/2x)


is related to the graph of the basic trigonometric function f(x)=tanx


.

Part I: What kind of reflection does the basic function experience? (2 points)

 

 

 

 

 

Part II: What is the vertical stretch factor of the function R(x)? (2 points)

 

Vertical shift ; none

 

 

 

Part III: What is the horizontal stretch factor of the function R(x)? (4 points)


1
Expert's answer
2021-05-02T10:01:21-0400

Step 1

Consider the functions 

r(x)=3tan(12x)r(x)=−3tan(\frac{1}{2}x)

f(x)=tanxf(x)=tanx


         

rx=−3tan12x               fx=tanx

 

 

Step 2

Consider a function f(x) and its transformed function is 

g(x)=af(bx)+dg(x)=af(bx)+d

Vertical stretch factor = |a|

Horizontal stretch factor = 1b\frac{1}{b}

Vertical shift = d


 

Step 3

Part I: What kind of reflection does the basic function experience?

 

Basic function f(x)=tanx

f(x)=tanx experience a reflation about origin.




Step 4

Part II: What is the vertical stretch factor of the function R(x)?

 

Vertical Stretch factor : 3

 

 

Vertical shift ; none

 

 

Step 5

Part III: What is the horizontal stretch factor of the function R(x)?

b=12b=\frac {1}{2}


Horizontal stretch factor = 1÷12=21 \div \frac{1}{2}=2



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