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)
Step 1
Consider the functions
rx=−3tan12x fx=tanx
Step 2
Consider a function f(x) and its transformed function is
Vertical stretch factor = |a|
Horizontal stretch factor =
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)?
Horizontal stretch factor =
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