Consider the function f \left( x \right) = \tan x graphed and the function g \left( x \right) = \tan \left(x - \dfrac{\pi}{3}\right).
The point A on the graph of f \left( x \right) has the coordinates \left(0, 0\right).
What are the coordinates of the corresponding point on the graph of g \left( x \right)?
The point B on the graph of f \left( x \right) has the coordinates \left(\dfrac{\pi}{4}, 1\right).
What are the coordinates of the corresponding point on the graph of g \left( x \right)?
The graph of f \left( x \right) has an asymptote passing through point C with coordinates \left(\dfrac{\pi}{2}, 0\right).
What are the coordinates of the corresponding point on the graph of g \left( x \right)?
Hence, apply a phase shift to the graph of f \left( x \right) = \tan x to sketch the graph of \\ g \left( x \right) = \tan \left(x - \dfrac{\pi}{3}\right) for 0 \leq x \leq 2 \pi.
On the same set of axes, sketch the graph of y = \tan x and y = \dfrac{1}{2} \tan x for -2 \pi \leq x \leq 2 \pi.
On the same set of axes, sketch the graphs of the functions f \left( x \right) = - \dfrac{1}{2} \tan x and \\g \left( x \right) = 2 \tan x, on the domain -\pi \leq x \leq \pi.
Consider the function y = - 4 \tan \dfrac{1}{5} \left(x + \dfrac{\pi}{4}\right).
Find the period of the function, giving your answer in radians.
Find the phase shift of the function, giving your answer in radians.
State the range of the function.
Consider the function y = 6 - 3 \tan \left(x + \dfrac{\pi}{3}\right).
Find the period of the function, giving your answer in radians.
Find the phase shift of the function, giving your answer in radians.
State the range of the function.
How has the graph y = \tan \left( 2 x - \dfrac{\pi}{4}\right) been transformed from y = \tan x?
For each of the functions below:
Find the y-intercept.
Find the value of y when x = \dfrac{\pi}{4}.
Find the period of the function.
Find the distance between the asymptotes of the function.
State the equation of the first asymptote of the function for x \geq 0.
State the equation of the first asymptote of the function for x \leq 0.
Sketch a graph of the function for -2 \pi \leq x \leq 2 \pi.
For each of the following functions:
Find the y-intercept.
Find the period of the function in radians.
Find the distance between the asymptotes of the function.
State the first asymptote of the function for x \geq 0
State the first asymptote of the function for x \leq 0
Sketch a graph of the function for -\pi \leq x \leq \pi.
Consider the equation y = \tan 9 x.
State the period of the function in radians.
Sketch the graph of the function y = \tan 9 x for 0 \leq x \leq \pi.
Consider the function y = \tan 7 x.
Complete the given table of values for the function.
Graph the function for -\dfrac{5\pi}{28}\leq x \leq \dfrac{5\pi}{28}.
| x | -\dfrac{\pi}{28} | 0 | \dfrac{\pi}{28} | \dfrac{3\pi}{28} | \dfrac{\pi}{7} | \dfrac{5\pi}{28} |
|---|---|---|---|---|---|---|
| y |
A function in the form f \left( x \right) = \tan b x has adjacent x-intercepts at x = \dfrac{13 \pi}{6} and x = \dfrac{9 \pi}{4}.
State the equation of the asymptote lying between the two x-intercepts.
Find the period of the function.
State the equation of the function.