Interactive practice questions
We want to identify how the coordinates of key points on the graph of $f\left(x\right)=\tan x$f(x)=tanx change as we apply a phase shift to produce the graph of $g\left(x\right)=\tan\left(x-\frac{\pi}{3}\right)$g(x)=tan(x−π3).
The point $A$A on the graph of $f\left(x\right)$f(x) has the coordinates $\left(0,0\right)$(0,0).
What are the coordinates of the corresponding point on the graph of $g\left(x\right)$g(x)? Give your answer in the form $\left(\editable{},\editable{}\right)$(,).
The point $B$B on the graph of $f\left(x\right)$f(x) has the coordinates $\left(\frac{\pi}{4},1\right)$(π4,1).
What are the coordinates of the corresponding point on the graph of $g\left(x\right)$g(x)? Give your answer in the form $\left(\editable{},\editable{}\right)$(,).
The graph of $f\left(x\right)$f(x) has an asymptote passing through point $C$C with coordinates $\left(\frac{\pi}{2},0\right)$(π2,0).
What are the coordinates of the corresponding point on the graph of $g\left(x\right)$g(x)? Give your answer in the form $\left(\editable{},\editable{}\right)$(,).
Using the answers from the previous parts, apply a phase shift to the graph of $f\left(x\right)=\tan x$f(x)=tanx to draw the graph of $g\left(x\right)=\tan\left(x-\frac{\pi}{3}\right)$g(x)=tan(x−π3).
Consider the function $y=5\tan x+3$y=5tanx+3.
Answer the following questions in radians, where appropriate.
The functions $f\left(x\right)=-\frac{1}{2}\tan x$f(x)=−12tanx and $g\left(x\right)=2\tan x$g(x)=2tanx are drawn on the same set of axes, shown below.
Consider the function $y=6-3\tan\left(x+\frac{\pi}{3}\right)$y=6−3tan(x+π3).