Question 510855: hi, i need help learning how to graph tangent functions
.. the function i was given was y= tan (x- pi/4)
.. if anyone you help explain it to me and even show a graph,
that would be great!
thanks
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Graphing tangent functions
I don't have the means to draw a graph but maybe I can show you how.
given function: y= tan (x- pi/4)
Standard equation for tangent function: y=tan(Bx-C), period=π/B, Phase shift=C/B
For given function:
B=1
period=π/1=π
1/4 period=π/4
phase shift=C/B=(π/4)/1=π/4 (to the right)
Graphing for one period:
Without a phase shift, the curve of tanx would start at -π/2 and end at π/2
tan(-π/2)=-∞(asymptote)
tan(-π/4)=-1
tan(0)=0
tan(π/4)=1
tan(π/2)=∞(asymptote)
so, now you have these ordered pairs to draw the basic tanx function:
(-π/2, -∞), (-π/4,-1), (0,0), (π/4,1), (π/2,∞)
But since the curve has shifted π/4 radians, π/4 must be added to each x-coordinate to plot the given tan function, y= tan (x- pi/4), as follows:
(-π/4, -∞), (0,-1), (π/4,0), (π/2,1), (3π/4,∞)
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