Answer to Question #182824 in Trigonometry for sasai

Question

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)

Answer 1

Step 1

Consider the functions 

$r(x)=−3tan(\frac{1}{2}x)$

$f(x)=tanx$

         

rx=−3tan12x               fx=tanx

 

 

Step 2

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

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

Vertical stretch factor = |a|

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

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)?

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

Horizontal stretch factor = $1 \div \frac{1}{2}=2$