Question 498863: Explain how the graph of R(x)= -3tan(1/2x) is related to the graph of the basic trignometric function F(x)=tanx.
What kind of reflection does the basic function experience?
What is the vertical stretch factor of the function R(x)?
What is the horizontal stretch factor of the function R(x)?
What is the period of the function R(x)?
What are the equations of the vertical asymptotes of this functions?
What are the zeros of this function
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Explain how the graph of R(x)= -3tan(1/2x) is related to the graph of the basic trignometric function F(x)=tanx.
What kind of reflection does the basic function experience?
What is the vertical stretch factor of the function R(x)?
What is the horizontal stretch factor of the function R(x)?
What is the period of the function R(x)?
What are the equations of the vertical asymptotes of this functions?
What are the zeros of this function
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Standard form of equation for tan function: y=tan(Bx-C), Period=π/B, phase-shift=C/B
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Compared to tan x, -3tan(1/2x), has a different period and its graph is stretched by -3, and reflected about the x-axis because of the negative sign.
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For each (x,y), the point (-x,-y) is also on the graph which means the basic tan graph has reflections about the origin or symmetry about the origin.
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R(x) has a vertical stretch of -3 units
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R(x) has a horizontal stretch of 2 as the period has increased from π to 2π.
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Period of R(x)=π/B=π/(1/2)=2π
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Vertical Asymptotes: x=±π [(tan(π/2)=sin(π/2)/cos(π/2)=1/0=u.d.]
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zeros or x-intercept: at 0 [tan(x/2)=0, x=0]
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note to student: To help you see this visually, I suggest you put R(x) on a graphing calculator or better yet, on a graphing program on your computer.
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